Nested sampling algorithm - Revision history

OAbot: Open access bot: arxiv updated in citation with #oabot.

2024-12-30T04:14:35Z

Open access bot: arxiv updated in citation with #oabot.

← Previous revision		Revision as of 04:14, 30 December 2024
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	The original procedure outlined by Skilling (given above in pseudocode) does not specify what specific Markov chain Monte Carlo algorithm should be used to choose new points with better likelihood.		The original procedure outlined by Skilling (given above in pseudocode) does not specify what specific Markov chain Monte Carlo algorithm should be used to choose new points with better likelihood.

	Skilling's own code examples (such as one in Sivia and Skilling (2006),<ref>{{cite book \| last=Sivia \| first=Devinderjit \| last2=Skilling \| first2=John \| title=Data Analysis: A Bayesian Tutorial \| publisher=Oxford University Press, USA \| publication-place=Oxford \| date=June 2006 \| isbn=978-0-19-856832-2 \| page=}}</ref> [https://www.inference.org.uk/bayesys/sivia/lighthouse.c available on Skilling's website]) chooses a random existing point and selects a nearby point chosen by a random distance from the existing point; if the likelihood is better, then the point is accepted, else it is rejected and the process repeated. Mukherjee et al. (2006)<ref name="mukherjee">{{cite journal \|last1= Mukherjee \|first1= P. \|last2= Parkinson \|first2= D. \|last3= Liddle \|first3= A.R. \|title= A Nested Sampling Algorithm for Cosmological Model Selection \|journal= Astrophysical Journal \|volume= 638 \|issue= 2 \|pages= 51–54 \|year= 2006 \|bibcode= 2006ApJ...638L..51M \|doi= 10.1086/501068\|arxiv= astro-ph/0508461\|s2cid= 6208051 }}</ref> found higher acceptance rates by selecting points randomly within an ellipsoid drawn around the existing points; this idea was refined into the MultiNest algorithm<ref name="multinest">{{cite journal \|last1= Feroz \|first1= F. \|last2= Hobson \|first2= M.P. \| last3=Bridges\|first3=M.\|title= MULTINEST: an efficient and robust Bayesian inference tool for cosmology and particle physics \|journal= MNRAS \|volume= 398 \|issue= 4 \|year= 2008 \|url= https://arxiv.org/abs/0809.3437 \|doi= 10.1111/j.1365-2966.2009.14548.x}}</ref> which handles multimodal posteriors better by grouping points into likelihood contours and drawing an ellipsoid for each contour.		Skilling's own code examples (such as one in Sivia and Skilling (2006),<ref>{{cite book \| last=Sivia \| first=Devinderjit \| last2=Skilling \| first2=John \| title=Data Analysis: A Bayesian Tutorial \| publisher=Oxford University Press, USA \| publication-place=Oxford \| date=June 2006 \| isbn=978-0-19-856832-2 \| page=}}</ref> [https://www.inference.org.uk/bayesys/sivia/lighthouse.c available on Skilling's website]) chooses a random existing point and selects a nearby point chosen by a random distance from the existing point; if the likelihood is better, then the point is accepted, else it is rejected and the process repeated. Mukherjee et al. (2006)<ref name="mukherjee">{{cite journal \|last1= Mukherjee \|first1= P. \|last2= Parkinson \|first2= D. \|last3= Liddle \|first3= A.R. \|title= A Nested Sampling Algorithm for Cosmological Model Selection \|journal= Astrophysical Journal \|volume= 638 \|issue= 2 \|pages= 51–54 \|year= 2006 \|bibcode= 2006ApJ...638L..51M \|doi= 10.1086/501068\|arxiv= astro-ph/0508461\|s2cid= 6208051 }}</ref> found higher acceptance rates by selecting points randomly within an ellipsoid drawn around the existing points; this idea was refined into the MultiNest algorithm<ref name="multinest">{{cite journal \|last1= Feroz \|first1= F. \|last2= Hobson \|first2= M.P. \| last3=Bridges\|first3=M.\|title= MULTINEST: an efficient and robust Bayesian inference tool for cosmology and particle physics \|journal= MNRAS \|volume= 398 \|issue= 4 \|year= 2008 \|url= https://arxiv.org/abs/0809.3437 \|doi= 10.1111/j.1365-2966.2009.14548.x\|arxiv= 0809.3437 }}</ref> which handles multimodal posteriors better by grouping points into likelihood contours and drawing an ellipsoid for each contour.

	==Implementations==		==Implementations==

BattyBot: Fixed reference date error(s) (see CS1 errors: dates for details) and AWB general fixes

2024-12-28T16:59:55Z

Fixed reference date error(s) (see CS1 errors: dates for details) and AWB general fixes

← Previous revision		Revision as of 16:59, 28 December 2024
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	== Choice of MCMC algorithm ==		== Choice of MCMC algorithm ==
	The original procedure outlined by Skilling (given above in pseudocode) does not specify what specific Markov chain Monte Carlo algorithm should be used to choose new points with better likelihood.		The original procedure outlined by Skilling (given above in pseudocode) does not specify what specific Markov chain Monte Carlo algorithm should be used to choose new points with better likelihood.

	Skilling's own code examples (such as one in Sivia and Skilling (2006)<ref>{{cite book \| last=Sivia \| first=Devinderjit \| last2=Skilling \| first2=John \| title=Data Analysis: A Bayesian Tutorial \| publisher=Oxford University Press, USA \| publication-place=Oxford \| date=2006~~-06~~ \| isbn=978-0-19-856832-2 \| page=}}</ref>, [https://www.inference.org.uk/bayesys/sivia/lighthouse.c available on Skilling's website]) chooses a random existing point and selects a nearby point chosen by a random distance from the existing point; if the likelihood is better, then the point is accepted, else it is rejected and the process repeated. Mukherjee et al. (2006)<ref name="mukherjee">{{cite journal \|last1= Mukherjee \|first1= P. \|last2= Parkinson \|first2= D. \|last3= Liddle \|first3= A.R. \|title= A Nested Sampling Algorithm for Cosmological Model Selection \|journal= Astrophysical Journal \|volume= 638 \|issue= 2 \|pages= 51–54 \|year= 2006 \|bibcode= 2006ApJ...638L..51M \|doi= 10.1086/501068\|arxiv= astro-ph/0508461\|s2cid= 6208051 }}</ref> found higher acceptance rates by selecting points randomly within an ellipsoid drawn around the existing points; this idea was refined into the MultiNest algorithm<ref name="multinest">{{cite journal \|last1= Feroz \|first1= F. \|last2= Hobson \|first2= M.P. \| last3=Bridges\|first3=M.\|title= MULTINEST: an efficient and robust Bayesian inference tool for cosmology and particle physics \|journal= MNRAS \|volume= 398 \|issue= 4 \|year= 2008 \|url= https://arxiv.org/abs/0809.3437 \|doi= 10.1111/j.1365-2966.2009.14548.x}}</ref> which handles multimodal posteriors better by grouping points into likelihood contours and drawing an ellipsoid for each contour.		Skilling's own code examples (such as one in Sivia and Skilling (2006),<ref>{{cite book \| last=Sivia \| first=Devinderjit \| last2=Skilling \| first2=John \| title=Data Analysis: A Bayesian Tutorial \| publisher=Oxford University Press, USA \| publication-place=Oxford \| date=June 2006 \| isbn=978-0-19-856832-2 \| page=}}</ref> [https://www.inference.org.uk/bayesys/sivia/lighthouse.c available on Skilling's website]) chooses a random existing point and selects a nearby point chosen by a random distance from the existing point; if the likelihood is better, then the point is accepted, else it is rejected and the process repeated. Mukherjee et al. (2006)<ref name="mukherjee">{{cite journal \|last1= Mukherjee \|first1= P. \|last2= Parkinson \|first2= D. \|last3= Liddle \|first3= A.R. \|title= A Nested Sampling Algorithm for Cosmological Model Selection \|journal= Astrophysical Journal \|volume= 638 \|issue= 2 \|pages= 51–54 \|year= 2006 \|bibcode= 2006ApJ...638L..51M \|doi= 10.1086/501068\|arxiv= astro-ph/0508461\|s2cid= 6208051 }}</ref> found higher acceptance rates by selecting points randomly within an ellipsoid drawn around the existing points; this idea was refined into the MultiNest algorithm<ref name="multinest">{{cite journal \|last1= Feroz \|first1= F. \|last2= Hobson \|first2= M.P. \| last3=Bridges\|first3=M.\|title= MULTINEST: an efficient and robust Bayesian inference tool for cosmology and particle physics \|journal= MNRAS \|volume= 398 \|issue= 4 \|year= 2008 \|url= https://arxiv.org/abs/0809.3437 \|doi= 10.1111/j.1365-2966.2009.14548.x}}</ref> which handles multimodal posteriors better by grouping points into likelihood contours and drawing an ellipsoid for each contour.

	==Implementations==		==Implementations==
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	* A highly modular [[Python (programming language)\|Python]] parallel example for [[statistical physics]] and [[condensed matter physics]] uses is [https://github.com/js850/nested_sampling on GitHub].		* A highly modular [[Python (programming language)\|Python]] parallel example for [[statistical physics]] and [[condensed matter physics]] uses is [https://github.com/js850/nested_sampling on GitHub].
	* pymatnest is a package designed for exploring the [[energy landscape]] of different materials, calculating thermodynamic variables at arbitrary temperatures and locating [[phase transitions]] is [https://github.com/libAtoms/pymatnest on GitHub]		* pymatnest is a package designed for exploring the [[energy landscape]] of different materials, calculating thermodynamic variables at arbitrary temperatures and locating [[phase transitions]] is [https://github.com/libAtoms/pymatnest on GitHub]
	* The MultiNest software package is capable of performing nested sampling on multi-modal posterior distributions.<ref name="multinest"></~~ref~~><ref name="feroz">{{cite journal \|last1= Feroz \|first1= F. \|last2= Hobson \|first2= M.P. \|title= Multimodal nested sampling: an efficient and robust alternative to Markov Chain Monte Carlo methods for astronomical data analyses \|journal= MNRAS \|volume= 384 \|issue= 2 \|pages= 449–463 \|year= 2008 \|url= http://adsabs.harvard.edu/cgi-bin/bib_query?arXiv:0704.3704 \|doi= 10.1111/j.1365-2966.2007.12353.x \|doi-access= free \|bibcode=2008MNRAS.384..449F \|arxiv= 0704.3704\|s2cid= 14226032 }}</ref> It has interfaces for C++, [[Fortran]] and Python inputs, and is [https://github.com/farhanferoz/MultiNest available on GitHub].		* The MultiNest software package is capable of performing nested sampling on multi-modal posterior distributions.<ref name="multinest" /><ref name="feroz">{{cite journal \|last1= Feroz \|first1= F. \|last2= Hobson \|first2= M.P. \|title= Multimodal nested sampling: an efficient and robust alternative to Markov Chain Monte Carlo methods for astronomical data analyses \|journal= MNRAS \|volume= 384 \|issue= 2 \|pages= 449–463 \|year= 2008 \|url= http://adsabs.harvard.edu/cgi-bin/bib_query?arXiv:0704.3704 \|doi= 10.1111/j.1365-2966.2007.12353.x \|doi-access= free \|bibcode=2008MNRAS.384..449F \|arxiv= 0704.3704\|s2cid= 14226032 }}</ref> It has interfaces for C++, [[Fortran]] and Python inputs, and is [https://github.com/farhanferoz/MultiNest available on GitHub].
	* PolyChord is another nested sampling software package [https://github.com/PolyChord/PolyChordLite available on GitHub]. PolyChord's computational efficiency scales better with an increase in the number of parameters than MultiNest, meaning PolyChord can be more efficient for high dimensional problems.<ref>{{cite journal \|last1=Handley \|first1=Will \|first2=Mike \|last2=Hobson \|first3=Anthony \|last3=Lasenby \|title=polychord: next-generation nested sampling \|journal=Monthly Notices of the Royal Astronomical Society \|date=2015 \|volume=453 \|issue=4 \|pages=4384–4398 \|doi=10.1093/mnras/stv1911 \|doi-access=free \|bibcode=2015MNRAS.453.4384H \|arxiv=1506.00171 \|s2cid=118882763 }}</ref> It has interfaces to likelihood functions written in Python, Fortran, C, or C++.		* PolyChord is another nested sampling software package [https://github.com/PolyChord/PolyChordLite available on GitHub]. PolyChord's computational efficiency scales better with an increase in the number of parameters than MultiNest, meaning PolyChord can be more efficient for high dimensional problems.<ref>{{cite journal \|last1=Handley \|first1=Will \|first2=Mike \|last2=Hobson \|first3=Anthony \|last3=Lasenby \|title=polychord: next-generation nested sampling \|journal=Monthly Notices of the Royal Astronomical Society \|date=2015 \|volume=453 \|issue=4 \|pages=4384–4398 \|doi=10.1093/mnras/stv1911 \|doi-access=free \|bibcode=2015MNRAS.453.4384H \|arxiv=1506.00171 \|s2cid=118882763 }}</ref> It has interfaces to likelihood functions written in Python, Fortran, C, or C++.
	* NestedSamplers.jl, a [[Julia (programming language)\|Julia]] package for implementing single- and multi-ellipsoidal nested sampling algorithms is [https://github.com/TuringLang/NestedSamplers.jl on GitHub].		* NestedSamplers.jl, a [[Julia (programming language)\|Julia]] package for implementing single- and multi-ellipsoidal nested sampling algorithms is [https://github.com/TuringLang/NestedSamplers.jl on GitHub].
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	==Applications==		==Applications==
	Since nested sampling was proposed in 2004, it has been used in many aspects of the field of [[astronomy]]. One paper suggested using nested sampling for [[cosmology\|cosmological]] [[model selection]] and object detection, as it "uniquely combines accuracy, general applicability and computational feasibility."<ref name="mukherjee"></~~ref~~> A refinement of the algorithm to handle multimodal posteriors has been suggested as a means to detect astronomical objects in extant datasets.<ref name="feroz">{{cite journal \|last1= Feroz \|first1= F. \|last2= Hobson \|first2= M.P. \|title= Multimodal nested sampling: an efficient and robust alternative to Markov Chain Monte Carlo methods for astronomical data analyses \|journal= MNRAS \|volume= 384 \|issue= 2 \|pages= 449–463 \|year= 2008 \|url= http:/~~/adsabs.harvard.edu/cgi-bin/bib_query?arXiv:0704.3704 \|doi= 10.1111/j.1365-2966.2007.12353.x \|doi-access= free \|bibcode=2008MNRAS.384..449F \|arxiv= 0704.3704\|s2cid= 14226032 }}</ref~~> Other applications of nested sampling are in the field of [[finite element updating]] where the algorithm is used to choose an optimal [[finite element]] model, and this was applied to [[structural dynamics]].<ref>{{cite journal \|last1= Mthembu \|first1= L. \|last2= Marwala \|first2= T. \|last3= Friswell \|first3= M.I. \|last4= Adhikari \|first4= S. \|title= Model selection in finite element model updating using the Bayesian evidence statistic \|journal= Mechanical Systems and Signal Processing \|volume= 25 \|issue= 7 \|pages= 2399–2412 \|year= 2011 \|doi=10.1016/j.ymssp.2011.04.001\|bibcode= 2011MSSP...25.2399M }}</ref> This sampling method has also been used in the field of materials modeling. It can be used to learn the [[Partition function (statistical mechanics)\|partition function]] from [[statistical mechanics]] and derive [[thermodynamics\|thermodynamic]] properties. <ref name="partay">{{cite journal\|last1=Partay\|first1=Livia B.\|year=2010\|title=Efficient Sampling of Atomic Configurational Spaces\|journal=The Journal of Physical Chemistry B\|volume=114\|issue=32\|pages=10502–10512\|doi=10.1021/jp1012973\|pmid=20701382\|arxiv=0906.3544\|s2cid=16834142}}</ref>		Since nested sampling was proposed in 2004, it has been used in many aspects of the field of [[astronomy]]. One paper suggested using nested sampling for [[cosmology\|cosmological]] [[model selection]] and object detection, as it "uniquely combines accuracy, general applicability and computational feasibility."<ref name="mukherjee" /> A refinement of the algorithm to handle multimodal posteriors has been suggested as a means to detect astronomical objects in extant datasets.<ref name="feroz"/> Other applications of nested sampling are in the field of [[finite element updating]] where the algorithm is used to choose an optimal [[finite element]] model, and this was applied to [[structural dynamics]].<ref>{{cite journal \|last1= Mthembu \|first1= L. \|last2= Marwala \|first2= T. \|last3= Friswell \|first3= M.I. \|last4= Adhikari \|first4= S. \|title= Model selection in finite element model updating using the Bayesian evidence statistic \|journal= Mechanical Systems and Signal Processing \|volume= 25 \|issue= 7 \|pages= 2399–2412 \|year= 2011 \|doi=10.1016/j.ymssp.2011.04.001\|bibcode= 2011MSSP...25.2399M }}</ref> This sampling method has also been used in the field of materials modeling. It can be used to learn the [[Partition function (statistical mechanics)\|partition function]] from [[statistical mechanics]] and derive [[thermodynamics\|thermodynamic]] properties.<ref name="partay">{{cite journal\|last1=Partay\|first1=Livia B.\|year=2010\|title=Efficient Sampling of Atomic Configurational Spaces\|journal=The Journal of Physical Chemistry B\|volume=114\|issue=32\|pages=10502–10512\|doi=10.1021/jp1012973\|pmid=20701382\|arxiv=0906.3544\|s2cid=16834142}}</ref>

	==Dynamic nested sampling==		==Dynamic nested sampling==

MinervaKizyna: /* Implementations */ fixed link text

2024-12-28T12:55:36Z

Implementations: fixed link text

← Previous revision		Revision as of 12:55, 28 December 2024
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	* Simple examples in [[C (programming language)\|C]], [[R (programming language)\|R]], or [[Python (programming language)\|Python]] are on [http://www.inference.phy.cam.ac.uk/bayesys/ John Skilling's website].		* Simple examples in [[C (programming language)\|C]], [[R (programming language)\|R]], or [[Python (programming language)\|Python]] are on [http://www.inference.phy.cam.ac.uk/bayesys/ John Skilling's website].
	* A [[Haskell (programming language)\|Haskell]] port of [http://hackage.haskell.org/package/NestedSampling the above simple codes is on Hackage].		* A [[Haskell (programming language)\|Haskell]] port of [http://hackage.haskell.org/package/NestedSampling the above simple codes is on Hackage].
	* An example in [[R (programming language)\|R]] originally designed for [[Curve fitting\|fitting]] [[Spectrum\|spectra]] is described on [http://www.mrao.cam.ac.uk/~bn204/galevol/speca/rnested.html ~~Nested sampling algorithm in R on~~ Bojan Nikolic's website] and is [https://github.com/bnikolic/ available on GitHub].		* An example in [[R (programming language)\|R]] originally designed for [[Curve fitting\|fitting]] [[Spectrum\|spectra]] is described on [http://www.mrao.cam.ac.uk/~bn204/galevol/speca/rnested.html Bojan Nikolic's website] and is [https://github.com/bnikolic/ available on GitHub].
	* A NestedSampler is part of the [[Python (programming language)\|Python]] toolbox BayesicFitting<ref name="kester">{{cite journal \|last1= Kester \|first1= D. \|last2= Mueller \|first2= M. \|title= BayesicFitting, a PYTHON toolbox for Bayesian fitting and evidence calculation.: Including a Nested Sampling implementation. \|journal= Astronomy and Computing \|volume= 37 \|pages= 100503 \|year= 2021 \| doi= 10.1016/j.ascom.2021.100503\|doi-access= free \|arxiv= 2109.11976 \|bibcode= 2021A&C....3700503K }}</ref> for generic model fitting and evidence calculation. It is [https://github.com/dokester/BayesicFitting available on GitHub].		* A NestedSampler is part of the [[Python (programming language)\|Python]] toolbox BayesicFitting<ref name="kester">{{cite journal \|last1= Kester \|first1= D. \|last2= Mueller \|first2= M. \|title= BayesicFitting, a PYTHON toolbox for Bayesian fitting and evidence calculation.: Including a Nested Sampling implementation. \|journal= Astronomy and Computing \|volume= 37 \|pages= 100503 \|year= 2021 \| doi= 10.1016/j.ascom.2021.100503\|doi-access= free \|arxiv= 2109.11976 \|bibcode= 2021A&C....3700503K }}</ref> for generic model fitting and evidence calculation. It is [https://github.com/dokester/BayesicFitting available on GitHub].
	* An implementation in [[C++]], named DIAMONDS, [https://github.com/JorisDeRidder/ is on GitHub].		* An implementation in [[C++]], named DIAMONDS, [https://github.com/JorisDeRidder/ is on GitHub].

MinervaKizyna: turned refs that were just external links into inline external links

2024-12-28T12:53:20Z

turned refs that were just external links into inline external links

MinervaKizyna: added section on how to choose new nested sampling points

2024-12-28T12:42:28Z

added section on how to choose new nested sampling points

← Previous revision		Revision as of 12:42, 28 December 2024
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	The idea is to subdivide the range of <math>f(\theta) = P(D\mid\theta,M)</math> and estimate, for each interval <math>[f(\theta_{i-1}), f(\theta_i)]</math>, how likely it is a priori that a randomly chosen <math>\theta</math> would map to this interval. This can be thought of as a Bayesian's way to numerically implement [[Lebesgue integration]].<ref name="Jasa">{{cite journal \|last1= Jasa\|first1= Tomislav \|last2= Xiang \|first2= Ning\|title= Nested sampling applied in Bayesian room-acoustics decay analysis \|journal= Journal of the Acoustical Society of America \|pages= 3251–3262 \|year= 2012 \|volume= 132 \|issue= 5 \|doi=10.1121/1.4754550\|pmid= 23145609 \|bibcode= 2012ASAJ..132.3251J\|s2cid= 20876510 }}</ref>		The idea is to subdivide the range of <math>f(\theta) = P(D\mid\theta,M)</math> and estimate, for each interval <math>[f(\theta_{i-1}), f(\theta_i)]</math>, how likely it is a priori that a randomly chosen <math>\theta</math> would map to this interval. This can be thought of as a Bayesian's way to numerically implement [[Lebesgue integration]].<ref name="Jasa">{{cite journal \|last1= Jasa\|first1= Tomislav \|last2= Xiang \|first2= Ning\|title= Nested sampling applied in Bayesian room-acoustics decay analysis \|journal= Journal of the Acoustical Society of America \|pages= 3251–3262 \|year= 2012 \|volume= 132 \|issue= 5 \|doi=10.1121/1.4754550\|pmid= 23145609 \|bibcode= 2012ASAJ..132.3251J\|s2cid= 20876510 }}</ref>

			== Choice of MCMC algorithm ==
			The original procedure outlined by Skilling (given above in pseudocode) does not specify what specific Markov chain Monte Carlo algorithm should be used to choose new points with better likelihood.

			Skilling's own code examples (such as one in Sivia and Skilling (2006)<ref>{{cite book \| last=Sivia \| first=Devinderjit \| last2=Skilling \| first2=John \| title=Data Analysis: A Bayesian Tutorial \| publisher=Oxford University Press, USA \| publication-place=Oxford \| date=2006-06 \| isbn=978-0-19-856832-2 \| page=}}</ref>, [https://www.inference.org.uk/bayesys/sivia/lighthouse.c available on Skilling's website]) chooses a random existing point and selects a nearby point chosen by a random distance from the existing point; if the likelihood is better, then the point is accepted, else it is rejected and the process repeated. Mukherjee et al. (2006)<ref name="mukherjee">{{cite journal \|last1= Mukherjee \|first1= P. \|last2= Parkinson \|first2= D. \|last3= Liddle \|first3= A.R. \|title= A Nested Sampling Algorithm for Cosmological Model Selection \|journal= Astrophysical Journal \|volume= 638 \|issue= 2 \|pages= 51–54 \|year= 2006 \|bibcode= 2006ApJ...638L..51M \|doi= 10.1086/501068\|arxiv= astro-ph/0508461\|s2cid= 6208051 }}</ref> found higher acceptance rates by selecting points randomly within an ellipsoid drawn around the existing points; this idea was refined into the MultiNest algorithm<ref name="multinest">{{cite journal \|last1= Feroz \|first1= F. \|last2= Hobson \|first2= M.P. \| last3=Bridges\|first3=M.\|title= MULTINEST: an efficient and robust Bayesian inference tool for cosmology and particle physics \|journal= MNRAS \|volume= 398 \|issue= 4 \|year= 2008 \|url= https://arxiv.org/abs/0809.3437 \|doi= 10.1111/j.1365-2966.2009.14548.x}}</ref> which handles multimodal posteriors better by grouping points into likelihood contours and drawing an ellipsoid for each contour.

	==Implementations==		==Implementations==
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	==Applications==		==Applications==
	Since nested sampling was proposed in 2004, it has been used in many aspects of the field of [[astronomy]]. One paper suggested using nested sampling for [[cosmology\|cosmological]] [[model selection]] and object detection, as it "uniquely combines accuracy, general applicability and computational feasibility."<ref name="mukherjee">{{cite journal \|last1= Mukherjee \|first1= P. \|last2= Parkinson \|first2= D. \|last3= Liddle \|first3= A.R. \|title= A Nested Sampling Algorithm for Cosmological Model Selection \|journal= Astrophysical Journal \|volume= 638 \|issue= 2 \|pages= 51–54 \|year= 2006 \|bibcode= 2006ApJ...638L..51M \|doi= 10.1086/501068\|arxiv= astro-ph/0508461\|s2cid= 6208051 }}</ref> A refinement of the algorithm to handle multimodal posteriors has been suggested as a means to detect astronomical objects in extant datasets.<ref name="feroz">{{cite journal \|last1= Feroz \|first1= F. \|last2= Hobson \|first2= M.P. \|title= Multimodal nested sampling: an efficient and robust alternative to Markov Chain Monte Carlo methods for astronomical data analyses \|journal= MNRAS \|volume= 384 \|issue= 2 \|pages= 449–463 \|year= 2008 \|url= http://adsabs.harvard.edu/cgi-bin/bib_query?arXiv:0704.3704 \|doi= 10.1111/j.1365-2966.2007.12353.x \|doi-access= free \|bibcode=2008MNRAS.384..449F \|arxiv= 0704.3704\|s2cid= 14226032 }}</ref> Other applications of nested sampling are in the field of [[finite element updating]] where the algorithm is used to choose an optimal [[finite element]] model, and this was applied to [[structural dynamics]].<ref>{{cite journal \|last1= Mthembu \|first1= L. \|last2= Marwala \|first2= T. \|last3= Friswell \|first3= M.I. \|last4= Adhikari \|first4= S. \|title= Model selection in finite element model updating using the Bayesian evidence statistic \|journal= Mechanical Systems and Signal Processing \|volume= 25 \|issue= 7 \|pages= 2399–2412 \|year= 2011 \|doi=10.1016/j.ymssp.2011.04.001\|bibcode= 2011MSSP...25.2399M }}</ref> This sampling method has also been used in the field of materials modeling. It can be used to learn the [[Partition function (statistical mechanics)\|partition function]] from [[statistical mechanics]] and derive [[thermodynamics\|thermodynamic]] properties. <ref name="partay">{{cite journal\|last1=Partay\|first1=Livia B.\|year=2010\|title=Efficient Sampling of Atomic Configurational Spaces\|journal=The Journal of Physical Chemistry B\|volume=114\|issue=32\|pages=10502–10512\|doi=10.1021/jp1012973\|pmid=20701382\|arxiv=0906.3544\|s2cid=16834142}}</ref>		Since nested sampling was proposed in 2004, it has been used in many aspects of the field of [[astronomy]]. One paper suggested using nested sampling for [[cosmology\|cosmological]] [[model selection]] and object detection, as it "uniquely combines accuracy, general applicability and computational feasibility."<ref name="mukherjee"></ref> A refinement of the algorithm to handle multimodal posteriors has been suggested as a means to detect astronomical objects in extant datasets.<ref name="feroz">{{cite journal \|last1= Feroz \|first1= F. \|last2= Hobson \|first2= M.P. \|title= Multimodal nested sampling: an efficient and robust alternative to Markov Chain Monte Carlo methods for astronomical data analyses \|journal= MNRAS \|volume= 384 \|issue= 2 \|pages= 449–463 \|year= 2008 \|url= http://adsabs.harvard.edu/cgi-bin/bib_query?arXiv:0704.3704 \|doi= 10.1111/j.1365-2966.2007.12353.x \|doi-access= free \|bibcode=2008MNRAS.384..449F \|arxiv= 0704.3704\|s2cid= 14226032 }}</ref> Other applications of nested sampling are in the field of [[finite element updating]] where the algorithm is used to choose an optimal [[finite element]] model, and this was applied to [[structural dynamics]].<ref>{{cite journal \|last1= Mthembu \|first1= L. \|last2= Marwala \|first2= T. \|last3= Friswell \|first3= M.I. \|last4= Adhikari \|first4= S. \|title= Model selection in finite element model updating using the Bayesian evidence statistic \|journal= Mechanical Systems and Signal Processing \|volume= 25 \|issue= 7 \|pages= 2399–2412 \|year= 2011 \|doi=10.1016/j.ymssp.2011.04.001\|bibcode= 2011MSSP...25.2399M }}</ref> This sampling method has also been used in the field of materials modeling. It can be used to learn the [[Partition function (statistical mechanics)\|partition function]] from [[statistical mechanics]] and derive [[thermodynamics\|thermodynamic]] properties. <ref name="partay">{{cite journal\|last1=Partay\|first1=Livia B.\|year=2010\|title=Efficient Sampling of Atomic Configurational Spaces\|journal=The Journal of Physical Chemistry B\|volume=114\|issue=32\|pages=10502–10512\|doi=10.1021/jp1012973\|pmid=20701382\|arxiv=0906.3544\|s2cid=16834142}}</ref>

	==Dynamic nested sampling==		==Dynamic nested sampling==

Citation bot: Added bibcode. | Use this bot. Report bugs. | Suggested by Dominic3203 | Category:Randomized algorithms | #UCB_Category 3/44

2024-12-15T06:26:01Z

Added bibcode. | Use this bot. Report bugs. | Suggested by Dominic3203 | Category:Randomized algorithms | #UCB_Category 3/44

← Previous revision		Revision as of 06:26, 15 December 2024
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	* A [[Haskell (programming language)\|Haskell]] port of the above simple codes is on Hackage.<ref>[http://hackage.haskell.org/package/NestedSampling Nested sampling algorithm in Haskell at Hackage]</ref>		* A [[Haskell (programming language)\|Haskell]] port of the above simple codes is on Hackage.<ref>[http://hackage.haskell.org/package/NestedSampling Nested sampling algorithm in Haskell at Hackage]</ref>
	* An example in [[R (programming language)\|R]] originally designed for [[Curve fitting\|fitting]] [[Spectrum\|spectra]] is described at <ref>[http://www.mrao.cam.ac.uk/~bn204/galevol/speca/rnested.html Nested sampling algorithm in R on Bojan Nikolic website]</ref> and is on GitHub.<ref>[https://github.com/bnikolic/RNested Nested sampling algorithm in R on GitHub]</ref>		* An example in [[R (programming language)\|R]] originally designed for [[Curve fitting\|fitting]] [[Spectrum\|spectra]] is described at <ref>[http://www.mrao.cam.ac.uk/~bn204/galevol/speca/rnested.html Nested sampling algorithm in R on Bojan Nikolic website]</ref> and is on GitHub.<ref>[https://github.com/bnikolic/RNested Nested sampling algorithm in R on GitHub]</ref>
	* A NestedSampler is part of the Python toolbox BayesicFitting <ref name="kester">{{cite journal \|last1= Kester \|first1= D. \|last2= Mueller \|first2= M. \|title= BayesicFitting, a PYTHON toolbox for Bayesian fitting and evidence calculation.: Including a Nested Sampling implementation. \|journal= Astronomy and Computing \|volume= 37 \|pages= 100503 \|year= 2021 \| doi= 10.1016/j.ascom.2021.100503\|doi-access= free \|arxiv= 2109.11976 }}</ref> for generic model fitting and evidence calculation. It is on Github <ref>[https://github.com/dokester/BayesicFitting Python toolbox containing a Nested sampling algorithm on GitHub]</ref>		* A NestedSampler is part of the Python toolbox BayesicFitting <ref name="kester">{{cite journal \|last1= Kester \|first1= D. \|last2= Mueller \|first2= M. \|title= BayesicFitting, a PYTHON toolbox for Bayesian fitting and evidence calculation.: Including a Nested Sampling implementation. \|journal= Astronomy and Computing \|volume= 37 \|pages= 100503 \|year= 2021 \| doi= 10.1016/j.ascom.2021.100503\|doi-access= free \|arxiv= 2109.11976 \|bibcode= 2021A&C....3700503K }}</ref> for generic model fitting and evidence calculation. It is on Github <ref>[https://github.com/dokester/BayesicFitting Python toolbox containing a Nested sampling algorithm on GitHub]</ref>
	* An example in [[C++]], named Diamonds, is on GitHub.<ref>[https://github.com/JorisDeRidder/DIAMONDS Nested sampling algorithm in C++ on GitHub]</ref>		* An example in [[C++]], named Diamonds, is on GitHub.<ref>[https://github.com/JorisDeRidder/DIAMONDS Nested sampling algorithm in C++ on GitHub]</ref>
	* A highly modular [[Python (programming language)\|Python]] parallel example for [[statistical physics]] and [[condensed matter physics]] uses is on GitHub.<ref>[https://github.com/js850/nested_sampling Nested sampling algorithm in Python on GitHub]</ref>		* A highly modular [[Python (programming language)\|Python]] parallel example for [[statistical physics]] and [[condensed matter physics]] uses is on GitHub.<ref>[https://github.com/js850/nested_sampling Nested sampling algorithm in Python on GitHub]</ref>

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← Previous revision		Revision as of 04:16, 4 January 2024
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	* A [[Haskell (programming language)\|Haskell]] port of the above simple codes is on Hackage.<ref>[http://hackage.haskell.org/package/NestedSampling Nested sampling algorithm in Haskell at Hackage]</ref>		* A [[Haskell (programming language)\|Haskell]] port of the above simple codes is on Hackage.<ref>[http://hackage.haskell.org/package/NestedSampling Nested sampling algorithm in Haskell at Hackage]</ref>
	* An example in [[R (programming language)\|R]] originally designed for [[Curve fitting\|fitting]] [[Spectrum\|spectra]] is described at <ref>[http://www.mrao.cam.ac.uk/~bn204/galevol/speca/rnested.html Nested sampling algorithm in R on Bojan Nikolic website]</ref> and is on GitHub.<ref>[https://github.com/bnikolic/RNested Nested sampling algorithm in R on GitHub]</ref>		* An example in [[R (programming language)\|R]] originally designed for [[Curve fitting\|fitting]] [[Spectrum\|spectra]] is described at <ref>[http://www.mrao.cam.ac.uk/~bn204/galevol/speca/rnested.html Nested sampling algorithm in R on Bojan Nikolic website]</ref> and is on GitHub.<ref>[https://github.com/bnikolic/RNested Nested sampling algorithm in R on GitHub]</ref>
	* A NestedSampler is part of the Python toolbox BayesicFitting <ref name="kester">{{cite journal \|last1= Kester \|first1= D. \|last2= Mueller \|first2= M. \|title= BayesicFitting, a PYTHON toolbox for Bayesian fitting and evidence calculation.: Including a Nested Sampling implementation. \|journal= Astronomy and Computing \|volume= 37 \|pages= 100503 \|year= 2021 \| doi= 10.1016/j.ascom.2021.100503\|doi-access= free }}</ref> for generic model fitting and evidence calculation. It is on Github <ref>[https://github.com/dokester/BayesicFitting Python toolbox containing a Nested sampling algorithm on GitHub]</ref>		* A NestedSampler is part of the Python toolbox BayesicFitting <ref name="kester">{{cite journal \|last1= Kester \|first1= D. \|last2= Mueller \|first2= M. \|title= BayesicFitting, a PYTHON toolbox for Bayesian fitting and evidence calculation.: Including a Nested Sampling implementation. \|journal= Astronomy and Computing \|volume= 37 \|pages= 100503 \|year= 2021 \| doi= 10.1016/j.ascom.2021.100503\|doi-access= free \|arxiv= 2109.11976 }}</ref> for generic model fitting and evidence calculation. It is on Github <ref>[https://github.com/dokester/BayesicFitting Python toolbox containing a Nested sampling algorithm on GitHub]</ref>
	* An example in [[C++]], named Diamonds, is on GitHub.<ref>[https://github.com/JorisDeRidder/DIAMONDS Nested sampling algorithm in C++ on GitHub]</ref>		* An example in [[C++]], named Diamonds, is on GitHub.<ref>[https://github.com/JorisDeRidder/DIAMONDS Nested sampling algorithm in C++ on GitHub]</ref>
	* A highly modular [[Python (programming language)\|Python]] parallel example for [[statistical physics]] and [[condensed matter physics]] uses is on GitHub.<ref>[https://github.com/js850/nested_sampling Nested sampling algorithm in Python on GitHub]</ref>		* A highly modular [[Python (programming language)\|Python]] parallel example for [[statistical physics]] and [[condensed matter physics]] uses is on GitHub.<ref>[https://github.com/js850/nested_sampling Nested sampling algorithm in Python on GitHub]</ref>

OAbot: Open access bot: doi updated in citation with #oabot.

2023-11-07T12:04:50Z

Open access bot: doi updated in citation with #oabot.

← Previous revision		Revision as of 12:04, 7 November 2023
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	* A [[Haskell (programming language)\|Haskell]] port of the above simple codes is on Hackage.<ref>[http://hackage.haskell.org/package/NestedSampling Nested sampling algorithm in Haskell at Hackage]</ref>		* A [[Haskell (programming language)\|Haskell]] port of the above simple codes is on Hackage.<ref>[http://hackage.haskell.org/package/NestedSampling Nested sampling algorithm in Haskell at Hackage]</ref>
	* An example in [[R (programming language)\|R]] originally designed for [[Curve fitting\|fitting]] [[Spectrum\|spectra]] is described at <ref>[http://www.mrao.cam.ac.uk/~bn204/galevol/speca/rnested.html Nested sampling algorithm in R on Bojan Nikolic website]</ref> and is on GitHub.<ref>[https://github.com/bnikolic/RNested Nested sampling algorithm in R on GitHub]</ref>		* An example in [[R (programming language)\|R]] originally designed for [[Curve fitting\|fitting]] [[Spectrum\|spectra]] is described at <ref>[http://www.mrao.cam.ac.uk/~bn204/galevol/speca/rnested.html Nested sampling algorithm in R on Bojan Nikolic website]</ref> and is on GitHub.<ref>[https://github.com/bnikolic/RNested Nested sampling algorithm in R on GitHub]</ref>
	* A NestedSampler is part of the Python toolbox BayesicFitting <ref name="kester">{{cite journal \|last1= Kester \|first1= D. \|last2= Mueller \|first2= M. \|title= BayesicFitting, a PYTHON toolbox for Bayesian fitting and evidence calculation.: Including a Nested Sampling implementation. \|journal= Astronomy and Computing \|volume= 37 \|pages= 100503 \|year= 2021 \| doi= 10.1016/j.ascom.2021.100503}}</ref> for generic model fitting and evidence calculation. It is on Github <ref>[https://github.com/dokester/BayesicFitting Python toolbox containing a Nested sampling algorithm on GitHub]</ref>		* A NestedSampler is part of the Python toolbox BayesicFitting <ref name="kester">{{cite journal \|last1= Kester \|first1= D. \|last2= Mueller \|first2= M. \|title= BayesicFitting, a PYTHON toolbox for Bayesian fitting and evidence calculation.: Including a Nested Sampling implementation. \|journal= Astronomy and Computing \|volume= 37 \|pages= 100503 \|year= 2021 \| doi= 10.1016/j.ascom.2021.100503\|doi-access= free }}</ref> for generic model fitting and evidence calculation. It is on Github <ref>[https://github.com/dokester/BayesicFitting Python toolbox containing a Nested sampling algorithm on GitHub]</ref>
	* An example in [[C++]], named Diamonds, is on GitHub.<ref>[https://github.com/JorisDeRidder/DIAMONDS Nested sampling algorithm in C++ on GitHub]</ref>		* An example in [[C++]], named Diamonds, is on GitHub.<ref>[https://github.com/JorisDeRidder/DIAMONDS Nested sampling algorithm in C++ on GitHub]</ref>
	* A highly modular [[Python (programming language)\|Python]] parallel example for [[statistical physics]] and [[condensed matter physics]] uses is on GitHub.<ref>[https://github.com/js850/nested_sampling Nested sampling algorithm in Python on GitHub]</ref>		* A highly modular [[Python (programming language)\|Python]] parallel example for [[statistical physics]] and [[condensed matter physics]] uses is on GitHub.<ref>[https://github.com/js850/nested_sampling Nested sampling algorithm in Python on GitHub]</ref>

Citation bot: Add: doi-access. Removed proxy/dead URL that duplicated identifier. | Use this bot. Report bugs. | #UCB_CommandLine

2023-10-25T11:05:09Z

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← Previous revision		Revision as of 11:05, 25 October 2023
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	In the limit <math>j \to \infty</math>, this estimator has a positive bias of order <math> 1 / N</math><ref>{{cite journal \|last= Walter \|first= Clement\| title=Point-process based Monte Carlo estimation\| journal=Statistics and Computing\|pages=219–236 \|year=2017\| volume=27\|doi=10.1007/s11222-015-9617-y \|arxiv=1412.6368\|s2cid= 14639080}}</ref> which can be removed by using <math>(1 - 1/N)</math> instead of the <math>\exp (-1/N)</math> in the above algorithm.		In the limit <math>j \to \infty</math>, this estimator has a positive bias of order <math> 1 / N</math><ref>{{cite journal \|last= Walter \|first= Clement\| title=Point-process based Monte Carlo estimation\| journal=Statistics and Computing\|pages=219–236 \|year=2017\| volume=27\|doi=10.1007/s11222-015-9617-y \|arxiv=1412.6368\|s2cid= 14639080}}</ref> which can be removed by using <math>(1 - 1/N)</math> instead of the <math>\exp (-1/N)</math> in the above algorithm.

	The idea is to subdivide the range of <math>f(\theta) = P(D\mid\theta,M)</math> and estimate, for each interval <math>[f(\theta_{i-1}), f(\theta_i)]</math>, how likely it is a priori that a randomly chosen <math>\theta</math> would map to this interval. This can be thought of as a Bayesian's way to numerically implement [[Lebesgue integration]].<ref name="Jasa">{{cite journal \|last1= Jasa\|first1= Tomislav \|last2= Xiang \|first2= Ning\|title= Nested sampling applied in Bayesian room-acoustics decay analysis \|journal= Journal of the Acoustical Society of America \|pages= 3251–3262 \|year= 2012 \|volume= 132 \|issue= 5 \|doi=10.1121/1.4754550\|pmid= 23145609 \|bibcode= 2012ASAJ..132.3251J\|s2cid= 20876510 ~~\|url= https://semanticscholar.org/paper/8225853110831e251aff26fc9b6431d0f2cc6e6c~~ }}</ref>		The idea is to subdivide the range of <math>f(\theta) = P(D\mid\theta,M)</math> and estimate, for each interval <math>[f(\theta_{i-1}), f(\theta_i)]</math>, how likely it is a priori that a randomly chosen <math>\theta</math> would map to this interval. This can be thought of as a Bayesian's way to numerically implement [[Lebesgue integration]].<ref name="Jasa">{{cite journal \|last1= Jasa\|first1= Tomislav \|last2= Xiang \|first2= Ning\|title= Nested sampling applied in Bayesian room-acoustics decay analysis \|journal= Journal of the Acoustical Society of America \|pages= 3251–3262 \|year= 2012 \|volume= 132 \|issue= 5 \|doi=10.1121/1.4754550\|pmid= 23145609 \|bibcode= 2012ASAJ..132.3251J\|s2cid= 20876510 }}</ref>

	==Implementations==		==Implementations==
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	* dyPolyChord: a software package which can be used with Python, C++ and Fortran likelihood and prior distributions.<ref>{{cite journal \|last1=Higson \|first1=Edward \|title=dyPolyChord: dynamic nested sampling with PolyChord \|journal=Journal of Open Source Software \|date=2018 \|volume=3 \|issue=29 \|page=965 \|doi=10.21105/joss.00965 \|doi-access=free }}</ref> dyPolyChord is available on GitHub.<ref>[https://github.com/ejhigson/dyPolyChord The dyPolyChord dynamic nested sampling software package on GitHub]</ref>		* dyPolyChord: a software package which can be used with Python, C++ and Fortran likelihood and prior distributions.<ref>{{cite journal \|last1=Higson \|first1=Edward \|title=dyPolyChord: dynamic nested sampling with PolyChord \|journal=Journal of Open Source Software \|date=2018 \|volume=3 \|issue=29 \|page=965 \|doi=10.21105/joss.00965 \|doi-access=free }}</ref> dyPolyChord is available on GitHub.<ref>[https://github.com/ejhigson/dyPolyChord The dyPolyChord dynamic nested sampling software package on GitHub]</ref>

	Dynamic nested sampling has been applied to a variety of scientific problems, including analysis of gravitational waves,<ref>{{cite journal \|last1=Ashton \|first1=Gregory \|title=Bilby: A User-friendly Bayesian Inference Library for Gravitational-wave Astronomy \|journal=The Astrophysical Journal Supplement Series \|date=2019 \|volume=241 \|issue=2 \|page=13 \|doi=10.3847/1538-4365/ab06fc \|display-authors=etal\|bibcode=2019ApJS..241...27A \|arxiv=1811.02042 \|s2cid=118677076 }}</ref> mapping distances in space<ref>{{cite journal \|last1=Zucker \|first1=Catherine \|title=Mapping Distances across the Perseus Molecular Cloud Using {CO} Observations, Stellar Photometry, and Gaia {DR}2 Parallax Measurements \|journal=The Astrophysical Journal \|date=2018 \|volume=869 \|issue=1 \|page=83 \|doi=10.3847/1538-4357/aae97c \|display-authors=etal\|arxiv=1803.08931 \|s2cid=119446622 }}</ref> and exoplanet detection.<ref>{{cite journal \|last1=Günther \|first1=Maximilian \|title=A super-Earth and two sub-Neptunes transiting the nearby and quiet M dwarf TOI-270 \|journal=Nature Astronomy \|date=2019 \|volume=3 \|issue=12 \|pages=1099–1108 \|doi=10.1038/s41550-019-0845-5 \|display-authors=etal\|bibcode=2019NatAs...3.1099G \|arxiv=1903.06107 \|s2cid=119286334 }}</ref>		Dynamic nested sampling has been applied to a variety of scientific problems, including analysis of gravitational waves,<ref>{{cite journal \|last1=Ashton \|first1=Gregory \|title=Bilby: A User-friendly Bayesian Inference Library for Gravitational-wave Astronomy \|journal=The Astrophysical Journal Supplement Series \|date=2019 \|volume=241 \|issue=2 \|page=13 \|doi=10.3847/1538-4365/ab06fc \|display-authors=etal\|bibcode=2019ApJS..241...27A \|arxiv=1811.02042 \|s2cid=118677076 \|doi-access=free }}</ref> mapping distances in space<ref>{{cite journal \|last1=Zucker \|first1=Catherine \|title=Mapping Distances across the Perseus Molecular Cloud Using {CO} Observations, Stellar Photometry, and Gaia {DR}2 Parallax Measurements \|journal=The Astrophysical Journal \|date=2018 \|volume=869 \|issue=1 \|page=83 \|doi=10.3847/1538-4357/aae97c \|display-authors=etal\|arxiv=1803.08931 \|s2cid=119446622 \|doi-access=free }}</ref> and exoplanet detection.<ref>{{cite journal \|last1=Günther \|first1=Maximilian \|title=A super-Earth and two sub-Neptunes transiting the nearby and quiet M dwarf TOI-270 \|journal=Nature Astronomy \|date=2019 \|volume=3 \|issue=12 \|pages=1099–1108 \|doi=10.1038/s41550-019-0845-5 \|display-authors=etal\|bibcode=2019NatAs...3.1099G \|arxiv=1903.06107 \|s2cid=119286334 }}</ref>

	==See also==		==See also==

← Previous revision		Revision as of 12:55, 28 December 2024
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	* Simple examples in [[C (programming language)\|C]], [[R (programming language)\|R]], or [[Python (programming language)\|Python]] are on [http://www.inference.phy.cam.ac.uk/bayesys/ John Skilling's website].		* Simple examples in [[C (programming language)\|C]], [[R (programming language)\|R]], or [[Python (programming language)\|Python]] are on [http://www.inference.phy.cam.ac.uk/bayesys/ John Skilling's website].
	* A [[Haskell (programming language)\|Haskell]] port of [http://hackage.haskell.org/package/NestedSampling the above simple codes is on Hackage].		* A [[Haskell (programming language)\|Haskell]] port of [http://hackage.haskell.org/package/NestedSampling the above simple codes is on Hackage].
	* An example in [[R (programming language)\|R]] originally designed for [[Curve fitting\|fitting]] [[Spectrum\|spectra]] is described on [http://www.mrao.cam.ac.uk/~bn204/galevol/speca/rnested.html ~~Nested sampling algorithm in R on~~ Bojan Nikolic's website] and is [https://github.com/bnikolic/ available on GitHub].		* An example in [[R (programming language)\|R]] originally designed for [[Curve fitting\|fitting]] [[Spectrum\|spectra]] is described on [http://www.mrao.cam.ac.uk/~bn204/galevol/speca/rnested.html Bojan Nikolic's website] and is [https://github.com/bnikolic/ available on GitHub].
	* A NestedSampler is part of the [[Python (programming language)\|Python]] toolbox BayesicFitting<ref name="kester">{{cite journal \|last1= Kester \|first1= D. \|last2= Mueller \|first2= M. \|title= BayesicFitting, a PYTHON toolbox for Bayesian fitting and evidence calculation.: Including a Nested Sampling implementation. \|journal= Astronomy and Computing \|volume= 37 \|pages= 100503 \|year= 2021 \| doi= 10.1016/j.ascom.2021.100503\|doi-access= free \|arxiv= 2109.11976 \|bibcode= 2021A&C....3700503K }}</ref> for generic model fitting and evidence calculation. It is [https://github.com/dokester/BayesicFitting available on GitHub].		* A NestedSampler is part of the [[Python (programming language)\|Python]] toolbox BayesicFitting<ref name="kester">{{cite journal \|last1= Kester \|first1= D. \|last2= Mueller \|first2= M. \|title= BayesicFitting, a PYTHON toolbox for Bayesian fitting and evidence calculation.: Including a Nested Sampling implementation. \|journal= Astronomy and Computing \|volume= 37 \|pages= 100503 \|year= 2021 \| doi= 10.1016/j.ascom.2021.100503\|doi-access= free \|arxiv= 2109.11976 \|bibcode= 2021A&C....3700503K }}</ref> for generic model fitting and evidence calculation. It is [https://github.com/dokester/BayesicFitting available on GitHub].
	* An implementation in [[C++]], named DIAMONDS, [https://github.com/JorisDeRidder/ is on GitHub].		* An implementation in [[C++]], named DIAMONDS, [https://github.com/JorisDeRidder/ is on GitHub].

← Previous revision		Revision as of 06:26, 15 December 2024
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	* A [[Haskell (programming language)\|Haskell]] port of the above simple codes is on Hackage.<ref>[http://hackage.haskell.org/package/NestedSampling Nested sampling algorithm in Haskell at Hackage]</ref>		* A [[Haskell (programming language)\|Haskell]] port of the above simple codes is on Hackage.<ref>[http://hackage.haskell.org/package/NestedSampling Nested sampling algorithm in Haskell at Hackage]</ref>
	* An example in [[R (programming language)\|R]] originally designed for [[Curve fitting\|fitting]] [[Spectrum\|spectra]] is described at <ref>[http://www.mrao.cam.ac.uk/~bn204/galevol/speca/rnested.html Nested sampling algorithm in R on Bojan Nikolic website]</ref> and is on GitHub.<ref>[https://github.com/bnikolic/RNested Nested sampling algorithm in R on GitHub]</ref>		* An example in [[R (programming language)\|R]] originally designed for [[Curve fitting\|fitting]] [[Spectrum\|spectra]] is described at <ref>[http://www.mrao.cam.ac.uk/~bn204/galevol/speca/rnested.html Nested sampling algorithm in R on Bojan Nikolic website]</ref> and is on GitHub.<ref>[https://github.com/bnikolic/RNested Nested sampling algorithm in R on GitHub]</ref>
	* A NestedSampler is part of the Python toolbox BayesicFitting <ref name="kester">{{cite journal \|last1= Kester \|first1= D. \|last2= Mueller \|first2= M. \|title= BayesicFitting, a PYTHON toolbox for Bayesian fitting and evidence calculation.: Including a Nested Sampling implementation. \|journal= Astronomy and Computing \|volume= 37 \|pages= 100503 \|year= 2021 \| doi= 10.1016/j.ascom.2021.100503\|doi-access= free \|arxiv= 2109.11976 }}</ref> for generic model fitting and evidence calculation. It is on Github <ref>[https://github.com/dokester/BayesicFitting Python toolbox containing a Nested sampling algorithm on GitHub]</ref>		* A NestedSampler is part of the Python toolbox BayesicFitting <ref name="kester">{{cite journal \|last1= Kester \|first1= D. \|last2= Mueller \|first2= M. \|title= BayesicFitting, a PYTHON toolbox for Bayesian fitting and evidence calculation.: Including a Nested Sampling implementation. \|journal= Astronomy and Computing \|volume= 37 \|pages= 100503 \|year= 2021 \| doi= 10.1016/j.ascom.2021.100503\|doi-access= free \|arxiv= 2109.11976 \|bibcode= 2021A&C....3700503K }}</ref> for generic model fitting and evidence calculation. It is on Github <ref>[https://github.com/dokester/BayesicFitting Python toolbox containing a Nested sampling algorithm on GitHub]</ref>
	* An example in [[C++]], named Diamonds, is on GitHub.<ref>[https://github.com/JorisDeRidder/DIAMONDS Nested sampling algorithm in C++ on GitHub]</ref>		* An example in [[C++]], named Diamonds, is on GitHub.<ref>[https://github.com/JorisDeRidder/DIAMONDS Nested sampling algorithm in C++ on GitHub]</ref>
	* A highly modular [[Python (programming language)\|Python]] parallel example for [[statistical physics]] and [[condensed matter physics]] uses is on GitHub.<ref>[https://github.com/js850/nested_sampling Nested sampling algorithm in Python on GitHub]</ref>		* A highly modular [[Python (programming language)\|Python]] parallel example for [[statistical physics]] and [[condensed matter physics]] uses is on GitHub.<ref>[https://github.com/js850/nested_sampling Nested sampling algorithm in Python on GitHub]</ref>

← Previous revision		Revision as of 04:16, 4 January 2024
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	* A [[Haskell (programming language)\|Haskell]] port of the above simple codes is on Hackage.<ref>[http://hackage.haskell.org/package/NestedSampling Nested sampling algorithm in Haskell at Hackage]</ref>		* A [[Haskell (programming language)\|Haskell]] port of the above simple codes is on Hackage.<ref>[http://hackage.haskell.org/package/NestedSampling Nested sampling algorithm in Haskell at Hackage]</ref>
	* An example in [[R (programming language)\|R]] originally designed for [[Curve fitting\|fitting]] [[Spectrum\|spectra]] is described at <ref>[http://www.mrao.cam.ac.uk/~bn204/galevol/speca/rnested.html Nested sampling algorithm in R on Bojan Nikolic website]</ref> and is on GitHub.<ref>[https://github.com/bnikolic/RNested Nested sampling algorithm in R on GitHub]</ref>		* An example in [[R (programming language)\|R]] originally designed for [[Curve fitting\|fitting]] [[Spectrum\|spectra]] is described at <ref>[http://www.mrao.cam.ac.uk/~bn204/galevol/speca/rnested.html Nested sampling algorithm in R on Bojan Nikolic website]</ref> and is on GitHub.<ref>[https://github.com/bnikolic/RNested Nested sampling algorithm in R on GitHub]</ref>
	* A NestedSampler is part of the Python toolbox BayesicFitting <ref name="kester">{{cite journal \|last1= Kester \|first1= D. \|last2= Mueller \|first2= M. \|title= BayesicFitting, a PYTHON toolbox for Bayesian fitting and evidence calculation.: Including a Nested Sampling implementation. \|journal= Astronomy and Computing \|volume= 37 \|pages= 100503 \|year= 2021 \| doi= 10.1016/j.ascom.2021.100503\|doi-access= free }}</ref> for generic model fitting and evidence calculation. It is on Github <ref>[https://github.com/dokester/BayesicFitting Python toolbox containing a Nested sampling algorithm on GitHub]</ref>		* A NestedSampler is part of the Python toolbox BayesicFitting <ref name="kester">{{cite journal \|last1= Kester \|first1= D. \|last2= Mueller \|first2= M. \|title= BayesicFitting, a PYTHON toolbox for Bayesian fitting and evidence calculation.: Including a Nested Sampling implementation. \|journal= Astronomy and Computing \|volume= 37 \|pages= 100503 \|year= 2021 \| doi= 10.1016/j.ascom.2021.100503\|doi-access= free \|arxiv= 2109.11976 }}</ref> for generic model fitting and evidence calculation. It is on Github <ref>[https://github.com/dokester/BayesicFitting Python toolbox containing a Nested sampling algorithm on GitHub]</ref>
	* An example in [[C++]], named Diamonds, is on GitHub.<ref>[https://github.com/JorisDeRidder/DIAMONDS Nested sampling algorithm in C++ on GitHub]</ref>		* An example in [[C++]], named Diamonds, is on GitHub.<ref>[https://github.com/JorisDeRidder/DIAMONDS Nested sampling algorithm in C++ on GitHub]</ref>
	* A highly modular [[Python (programming language)\|Python]] parallel example for [[statistical physics]] and [[condensed matter physics]] uses is on GitHub.<ref>[https://github.com/js850/nested_sampling Nested sampling algorithm in Python on GitHub]</ref>		* A highly modular [[Python (programming language)\|Python]] parallel example for [[statistical physics]] and [[condensed matter physics]] uses is on GitHub.<ref>[https://github.com/js850/nested_sampling Nested sampling algorithm in Python on GitHub]</ref>

← Previous revision		Revision as of 12:53, 28 December 2024
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	==Implementations==		==Implementations==
	Example implementations demonstrating the nested sampling algorithm are publicly available for download, written in several [[programming language]]s.		Example implementations demonstrating the nested sampling algorithm are publicly available for download, written in several [[programming language]]s.
	* Simple examples in [[C (programming language)\|C]], [[R (programming language)\|R]], or [[Python (programming language)\|Python]] are on ~~John Skilling's website.<ref>~~[http://www.inference.phy.cam.ac.uk/bayesys/ John Skilling website]~~</ref>~~		* Simple examples in [[C (programming language)\|C]], [[R (programming language)\|R]], or [[Python (programming language)\|Python]] are on [http://www.inference.phy.cam.ac.uk/bayesys/ John Skilling's website].
	* A [[Haskell (programming language)\|Haskell]] port of ~~the above simple codes is on Hackage.<ref>~~[http://hackage.haskell.org/package/NestedSampling ~~Nested~~ ~~sampling~~ ~~algorithm~~ in ~~Haskell~~ at Hackage]~~</ref>~~		* A [[Haskell (programming language)\|Haskell]] port of [http://hackage.haskell.org/package/NestedSampling the above simple codes is on Hackage].
	* An example in [[R (programming language)\|R]] originally designed for [[Curve fitting\|fitting]] [[Spectrum\|spectra]] is described at ~~<ref>~~[http://www.mrao.cam.ac.uk/~bn204/galevol/speca/rnested.html Nested sampling algorithm in R on Bojan Nikolic website]~~</ref>~~ and is ~~on GitHub.<ref>~~[https://github.com/bnikolic/~~RNested~~ ~~Nested sampling algorithm in R~~ on GitHub]~~</ref>~~		* An example in [[R (programming language)\|R]] originally designed for [[Curve fitting\|fitting]] [[Spectrum\|spectra]] is described on [http://www.mrao.cam.ac.uk/~bn204/galevol/speca/rnested.html Nested sampling algorithm in R on Bojan Nikolic's website] and is [https://github.com/bnikolic/ available on GitHub].
	* A NestedSampler is part of the Python toolbox BayesicFitting <ref name="kester">{{cite journal \|last1= Kester \|first1= D. \|last2= Mueller \|first2= M. \|title= BayesicFitting, a PYTHON toolbox for Bayesian fitting and evidence calculation.: Including a Nested Sampling implementation. \|journal= Astronomy and Computing \|volume= 37 \|pages= 100503 \|year= 2021 \| doi= 10.1016/j.ascom.2021.100503\|doi-access= free \|arxiv= 2109.11976 \|bibcode= 2021A&C....3700503K }}</ref> for generic model fitting and evidence calculation. It is ~~on Github <ref>~~[https://github.com/dokester/BayesicFitting ~~Python toolbox containing a Nested sampling algorithm~~ on GitHub]~~</ref>~~		* A NestedSampler is part of the [[Python (programming language)\|Python]] toolbox BayesicFitting<ref name="kester">{{cite journal \|last1= Kester \|first1= D. \|last2= Mueller \|first2= M. \|title= BayesicFitting, a PYTHON toolbox for Bayesian fitting and evidence calculation.: Including a Nested Sampling implementation. \|journal= Astronomy and Computing \|volume= 37 \|pages= 100503 \|year= 2021 \| doi= 10.1016/j.ascom.2021.100503\|doi-access= free \|arxiv= 2109.11976 \|bibcode= 2021A&C....3700503K }}</ref> for generic model fitting and evidence calculation. It is [https://github.com/dokester/BayesicFitting available on GitHub].
	* An ~~example~~ in [[C++]], named ~~Diamonds~~, ~~is on GitHub.<ref>~~[https://github.com/JorisDeRidder/~~DIAMONDS~~ ~~Nested sampling algorithm in C++~~ on GitHub]~~</ref>~~		* An implementation in [[C++]], named DIAMONDS, [https://github.com/JorisDeRidder/ is on GitHub].
	* A highly modular [[Python (programming language)\|Python]] parallel example for [[statistical physics]] and [[condensed matter physics]] uses is ~~on GitHub.<ref>~~[https://github.com/js850/nested_sampling ~~Nested sampling algorithm in Python~~ on GitHub]~~</ref>~~		* A highly modular [[Python (programming language)\|Python]] parallel example for [[statistical physics]] and [[condensed matter physics]] uses is [https://github.com/js850/nested_sampling on GitHub].
	* pymatnest is a ~~[[Python (programming language)\|Python]]~~ package designed for exploring the [[energy landscape]] of different materials, calculating thermodynamic variables at arbitrary temperatures and locating [[phase transitions]] is ~~on GitHub.<ref>~~[https://github.com/libAtoms/pymatnest ~~Nested sampling algorithm for materials simulation~~ on GitHub]~~</ref>~~		* pymatnest is a package designed for exploring the [[energy landscape]] of different materials, calculating thermodynamic variables at arbitrary temperatures and locating [[phase transitions]] is [https://github.com/libAtoms/pymatnest on GitHub]
	* The MultiNest software package is capable of performing nested sampling on multi-modal posterior distributions.<ref name="feroz">{{cite journal \|last1= Feroz \|first1= F. \|last2= Hobson \|first2= M.P. \|title= Multimodal nested sampling: an efficient and robust alternative to Markov Chain Monte Carlo methods for astronomical data analyses \|journal= MNRAS \|volume= 384 \|issue= 2 \|pages= 449–463 \|year= 2008 \|url= http://adsabs.harvard.edu/cgi-bin/bib_query?arXiv:0704.3704 \|doi= 10.1111/j.1365-2966.2007.12353.x \|doi-access= free \|bibcode=2008MNRAS.384..449F \|arxiv= 0704.3704\|s2cid= 14226032 }}</ref> It has interfaces for C++, Fortran and Python inputs, and is ~~available on GitHub.<ref>~~[https://github.com/farhanferoz/MultiNest ~~The MultiNest nested sampling software package~~ on GitHub]~~</ref>~~		* The MultiNest software package is capable of performing nested sampling on multi-modal posterior distributions.<ref name="multinest"></ref><ref name="feroz">{{cite journal \|last1= Feroz \|first1= F. \|last2= Hobson \|first2= M.P. \|title= Multimodal nested sampling: an efficient and robust alternative to Markov Chain Monte Carlo methods for astronomical data analyses \|journal= MNRAS \|volume= 384 \|issue= 2 \|pages= 449–463 \|year= 2008 \|url= http://adsabs.harvard.edu/cgi-bin/bib_query?arXiv:0704.3704 \|doi= 10.1111/j.1365-2966.2007.12353.x \|doi-access= free \|bibcode=2008MNRAS.384..449F \|arxiv= 0704.3704\|s2cid= 14226032 }}</ref> It has interfaces for C++, [[Fortran]] and Python inputs, and is [https://github.com/farhanferoz/MultiNest available on GitHub].
	* PolyChord is another nested sampling software package ~~available on GitHub.<ref>~~[https://github.com/PolyChord/PolyChordLite ~~The PolyChord nested sampling software package~~ on GitHub]~~</ref>~~ PolyChord's computational efficiency scales better with an increase in the number of parameters than MultiNest, meaning PolyChord can be more efficient for high dimensional problems.<ref>{{cite journal \|last1=Handley \|first1=Will \|first2=Mike \|last2=Hobson \|first3=Anthony \|last3=Lasenby \|title=polychord: next-generation nested sampling \|journal=Monthly Notices of the Royal Astronomical Society \|date=2015 \|volume=453 \|issue=4 \|pages=4384–4398 \|doi=10.1093/mnras/stv1911 \|doi-access=free \|bibcode=2015MNRAS.453.4384H \|arxiv=1506.00171 \|s2cid=118882763 }}</ref>		* PolyChord is another nested sampling software package [https://github.com/PolyChord/PolyChordLite available on GitHub]. PolyChord's computational efficiency scales better with an increase in the number of parameters than MultiNest, meaning PolyChord can be more efficient for high dimensional problems.<ref>{{cite journal \|last1=Handley \|first1=Will \|first2=Mike \|last2=Hobson \|first3=Anthony \|last3=Lasenby \|title=polychord: next-generation nested sampling \|journal=Monthly Notices of the Royal Astronomical Society \|date=2015 \|volume=453 \|issue=4 \|pages=4384–4398 \|doi=10.1093/mnras/stv1911 \|doi-access=free \|bibcode=2015MNRAS.453.4384H \|arxiv=1506.00171 \|s2cid=118882763 }}</ref> It has interfaces to likelihood functions written in Python, Fortran, C, or C++.
	* NestedSamplers.jl a [[Julia (programming language)\|Julia]] package for implementing single- and multi-ellipsoidal nested sampling algorithms is ~~on GitHub.<ref>~~[https://github.com/TuringLang/NestedSamplers.jl ~~Implementations of single and multi-ellipsoid nested sampling in Julia~~ on GitHub]~~</ref>~~		* NestedSamplers.jl, a [[Julia (programming language)\|Julia]] package for implementing single- and multi-ellipsoidal nested sampling algorithms is [https://github.com/TuringLang/NestedSamplers.jl on GitHub].
	* [https://www.cse-lab.ethz.ch/korali/ Korali] is a high-performance framework for uncertainty quantification, optimization, and deep reinforcement learning, which also implements nested sampling.		* [https://www.cse-lab.ethz.ch/korali/ Korali] is a high-performance framework for uncertainty quantification, optimization, and deep reinforcement learning, which also implements nested sampling.

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	Publicly available dynamic nested sampling software packages include:		Publicly available dynamic nested sampling software packages include:
	* {{Proper name\|dynesty}} - a Python implementation of dynamic nested sampling which can be ~~downloaded from GitHub.<ref>~~[https://github.com/joshspeagle/dynesty ~~The~~ ~~dynesty nested sampling software package on~~ GitHub]~~</ref>~~<ref>{{cite journal \|last=Speagle \|first=Joshua \|title=dynesty: A Dynamic Nested Sampling Package for Estimating Bayesian Posteriors and Evidences \|journal=Monthly Notices of the Royal Astronomical Society \|year=2020 \|volume=493 \|issue=3 \|pages=3132–3158 \|doi=10.1093/mnras/staa278 \|doi-access=free \|arxiv=1904.02180\|s2cid=102354337 }}</ref>		* {{Proper name\|dynesty}} - a Python implementation of dynamic nested sampling which can be [https://github.com/joshspeagle/dynesty downloaded from GitHub].<ref>{{cite journal \|last=Speagle \|first=Joshua \|title=dynesty: A Dynamic Nested Sampling Package for Estimating Bayesian Posteriors and Evidences \|journal=Monthly Notices of the Royal Astronomical Society \|year=2020 \|volume=493 \|issue=3 \|pages=3132–3158 \|doi=10.1093/mnras/staa278 \|doi-access=free \|arxiv=1904.02180\|s2cid=102354337 }}</ref>
	* dyPolyChord: a software package which can be used with Python, C++ and Fortran likelihood and prior distributions.<ref>{{cite journal \|last1=Higson \|first1=Edward \|title=dyPolyChord: dynamic nested sampling with PolyChord \|journal=Journal of Open Source Software \|date=2018 \|volume=3 \|issue=29 \|page=965 \|doi=10.21105/joss.00965 \|doi-access=free }}</ref> dyPolyChord is ~~available on GitHub.<ref>~~[https://github.com/ejhigson/dyPolyChord ~~The dyPolyChord dynamic nested sampling software package~~ on GitHub]~~</ref>~~		* dyPolyChord: a software package which can be used with Python, C++ and Fortran likelihood and prior distributions.<ref>{{cite journal \|last1=Higson \|first1=Edward \|title=dyPolyChord: dynamic nested sampling with PolyChord \|journal=Journal of Open Source Software \|date=2018 \|volume=3 \|issue=29 \|page=965 \|doi=10.21105/joss.00965 \|doi-access=free }}</ref> dyPolyChord is [https://github.com/ejhigson/dyPolyChord available on GitHub].

	Dynamic nested sampling has been applied to a variety of scientific problems, including analysis of gravitational waves,<ref>{{cite journal \|last1=Ashton \|first1=Gregory \|title=Bilby: A User-friendly Bayesian Inference Library for Gravitational-wave Astronomy \|journal=The Astrophysical Journal Supplement Series \|date=2019 \|volume=241 \|issue=2 \|page=13 \|doi=10.3847/1538-4365/ab06fc \|display-authors=etal\|bibcode=2019ApJS..241...27A \|arxiv=1811.02042 \|s2cid=118677076 \|doi-access=free }}</ref> mapping distances in space<ref>{{cite journal \|last1=Zucker \|first1=Catherine \|title=Mapping Distances across the Perseus Molecular Cloud Using {CO} Observations, Stellar Photometry, and Gaia {DR}2 Parallax Measurements \|journal=The Astrophysical Journal \|date=2018 \|volume=869 \|issue=1 \|page=83 \|doi=10.3847/1538-4357/aae97c \|display-authors=etal\|arxiv=1803.08931 \|s2cid=119446622 \|doi-access=free }}</ref> and exoplanet detection.<ref>{{cite journal \|last1=Günther \|first1=Maximilian \|title=A super-Earth and two sub-Neptunes transiting the nearby and quiet M dwarf TOI-270 \|journal=Nature Astronomy \|date=2019 \|volume=3 \|issue=12 \|pages=1099–1108 \|doi=10.1038/s41550-019-0845-5 \|display-authors=etal\|bibcode=2019NatAs...3.1099G \|arxiv=1903.06107 \|s2cid=119286334 }}</ref>		Dynamic nested sampling has been applied to a variety of scientific problems, including analysis of gravitational waves,<ref>{{cite journal \|last1=Ashton \|first1=Gregory \|title=Bilby: A User-friendly Bayesian Inference Library for Gravitational-wave Astronomy \|journal=The Astrophysical Journal Supplement Series \|date=2019 \|volume=241 \|issue=2 \|page=13 \|doi=10.3847/1538-4365/ab06fc \|display-authors=etal\|bibcode=2019ApJS..241...27A \|arxiv=1811.02042 \|s2cid=118677076 \|doi-access=free }}</ref> mapping distances in space<ref>{{cite journal \|last1=Zucker \|first1=Catherine \|title=Mapping Distances across the Perseus Molecular Cloud Using {CO} Observations, Stellar Photometry, and Gaia {DR}2 Parallax Measurements \|journal=The Astrophysical Journal \|date=2018 \|volume=869 \|issue=1 \|page=83 \|doi=10.3847/1538-4357/aae97c \|display-authors=etal\|arxiv=1803.08931 \|s2cid=119446622 \|doi-access=free }}</ref> and exoplanet detection.<ref>{{cite journal \|last1=Günther \|first1=Maximilian \|title=A super-Earth and two sub-Neptunes transiting the nearby and quiet M dwarf TOI-270 \|journal=Nature Astronomy \|date=2019 \|volume=3 \|issue=12 \|pages=1099–1108 \|doi=10.1038/s41550-019-0845-5 \|display-authors=etal\|bibcode=2019NatAs...3.1099G \|arxiv=1903.06107 \|s2cid=119286334 }}</ref>

← Previous revision		Revision as of 14:08, 19 September 2024
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	* A highly modular [[Python (programming language)\|Python]] parallel example for [[statistical physics]] and [[condensed matter physics]] uses is on GitHub.<ref>[https://github.com/js850/nested_sampling Nested sampling algorithm in Python on GitHub]</ref>		* A highly modular [[Python (programming language)\|Python]] parallel example for [[statistical physics]] and [[condensed matter physics]] uses is on GitHub.<ref>[https://github.com/js850/nested_sampling Nested sampling algorithm in Python on GitHub]</ref>
	* pymatnest is a [[Python (programming language)\|Python]] package designed for exploring the [[energy landscape]] of different materials, calculating thermodynamic variables at arbitrary temperatures and locating [[phase transitions]] is on GitHub.<ref>[https://github.com/libAtoms/pymatnest Nested sampling algorithm for materials simulation on GitHub]</ref>		* pymatnest is a [[Python (programming language)\|Python]] package designed for exploring the [[energy landscape]] of different materials, calculating thermodynamic variables at arbitrary temperatures and locating [[phase transitions]] is on GitHub.<ref>[https://github.com/libAtoms/pymatnest Nested sampling algorithm for materials simulation on GitHub]</ref>
	* The MultiNest software package is capable of performing nested sampling on multi-modal posterior distributions.<ref name="feroz">{{cite journal \|last1= Feroz \|first1= F. \|last2= Hobson \|first2= M.P. \|title= Multimodal nested sampling: an efficient and robust alternative to Markov Chain Monte Carlo methods for astronomical data analyses \|journal= MNRAS \|volume= 384 \|issue= 2 \|pages= 449–463 \|year= 2008 \|url= http://adsabs.harvard.edu/cgi-bin/bib_query?arXiv:0704.3704 \|doi= 10.1111/j.1365-2966.2007.12353.x \|bibcode=2008MNRAS.384..449F \|arxiv= 0704.3704\|s2cid= 14226032 }}</ref> It has interfaces for C++, Fortran and Python inputs, and is available on GitHub.<ref>[https://github.com/farhanferoz/MultiNest The MultiNest nested sampling software package on GitHub]</ref>		* The MultiNest software package is capable of performing nested sampling on multi-modal posterior distributions.<ref name="feroz">{{cite journal \|last1= Feroz \|first1= F. \|last2= Hobson \|first2= M.P. \|title= Multimodal nested sampling: an efficient and robust alternative to Markov Chain Monte Carlo methods for astronomical data analyses \|journal= MNRAS \|volume= 384 \|issue= 2 \|pages= 449–463 \|year= 2008 \|url= http://adsabs.harvard.edu/cgi-bin/bib_query?arXiv:0704.3704 \|doi= 10.1111/j.1365-2966.2007.12353.x \|doi-access= free \|bibcode=2008MNRAS.384..449F \|arxiv= 0704.3704\|s2cid= 14226032 }}</ref> It has interfaces for C++, Fortran and Python inputs, and is available on GitHub.<ref>[https://github.com/farhanferoz/MultiNest The MultiNest nested sampling software package on GitHub]</ref>
	* PolyChord is another nested sampling software package available on GitHub.<ref>[https://github.com/PolyChord/PolyChordLite The PolyChord nested sampling software package on GitHub]</ref> PolyChord's computational efficiency scales better with an increase in the number of parameters than MultiNest, meaning PolyChord can be more efficient for high dimensional problems.<ref>{{cite journal \|last1=Handley \|first1=Will \|first2=Mike \|last2=Hobson \|first3=Anthony \|last3=Lasenby \|title=polychord: next-generation nested sampling \|journal=Monthly Notices of the Royal Astronomical Society \|date=2015 \|volume=453 \|issue=4 \|pages=4384–4398 \|doi=10.1093/mnras/stv1911 \|bibcode=2015MNRAS.453.4384H \|arxiv=1506.00171 \|s2cid=118882763 }}</ref>		* PolyChord is another nested sampling software package available on GitHub.<ref>[https://github.com/PolyChord/PolyChordLite The PolyChord nested sampling software package on GitHub]</ref> PolyChord's computational efficiency scales better with an increase in the number of parameters than MultiNest, meaning PolyChord can be more efficient for high dimensional problems.<ref>{{cite journal \|last1=Handley \|first1=Will \|first2=Mike \|last2=Hobson \|first3=Anthony \|last3=Lasenby \|title=polychord: next-generation nested sampling \|journal=Monthly Notices of the Royal Astronomical Society \|date=2015 \|volume=453 \|issue=4 \|pages=4384–4398 \|doi=10.1093/mnras/stv1911 \|doi-access=free \|bibcode=2015MNRAS.453.4384H \|arxiv=1506.00171 \|s2cid=118882763 }}</ref>
	* NestedSamplers.jl a [[Julia (programming language)\|Julia]] package for implementing single- and multi-ellipsoidal nested sampling algorithms is on GitHub.<ref>[https://github.com/TuringLang/NestedSamplers.jl Implementations of single and multi-ellipsoid nested sampling in Julia on GitHub]</ref>		* NestedSamplers.jl a [[Julia (programming language)\|Julia]] package for implementing single- and multi-ellipsoidal nested sampling algorithms is on GitHub.<ref>[https://github.com/TuringLang/NestedSamplers.jl Implementations of single and multi-ellipsoid nested sampling in Julia on GitHub]</ref>
	* [https://www.cse-lab.ethz.ch/korali/ Korali] is a high-performance framework for uncertainty quantification, optimization, and deep reinforcement learning, which also implements nested sampling.		* [https://www.cse-lab.ethz.ch/korali/ Korali] is a high-performance framework for uncertainty quantification, optimization, and deep reinforcement learning, which also implements nested sampling.

	==Applications==		==Applications==
	Since nested sampling was proposed in 2004, it has been used in many aspects of the field of [[astronomy]]. One paper suggested using nested sampling for [[cosmology\|cosmological]] [[model selection]] and object detection, as it "uniquely combines accuracy, general applicability and computational feasibility."<ref name="mukherjee">{{cite journal \|last1= Mukherjee \|first1= P. \|last2= Parkinson \|first2= D. \|last3= Liddle \|first3= A.R. \|title= A Nested Sampling Algorithm for Cosmological Model Selection \|journal= Astrophysical Journal \|volume= 638 \|issue= 2 \|pages= 51–54 \|year= 2006 \|bibcode= 2006ApJ...638L..51M \|doi= 10.1086/501068\|arxiv= astro-ph/0508461\|s2cid= 6208051 }}</ref> A refinement of the algorithm to handle multimodal posteriors has been suggested as a means to detect astronomical objects in extant datasets.<ref name="feroz">{{cite journal \|last1= Feroz \|first1= F. \|last2= Hobson \|first2= M.P. \|title= Multimodal nested sampling: an efficient and robust alternative to Markov Chain Monte Carlo methods for astronomical data analyses \|journal= MNRAS \|volume= 384 \|issue= 2 \|pages= 449–463 \|year= 2008 \|url= http://adsabs.harvard.edu/cgi-bin/bib_query?arXiv:0704.3704 \|doi= 10.1111/j.1365-2966.2007.12353.x \|bibcode=2008MNRAS.384..449F \|arxiv= 0704.3704\|s2cid= 14226032 }}</ref> Other applications of nested sampling are in the field of [[finite element updating]] where the algorithm is used to choose an optimal [[finite element]] model, and this was applied to [[structural dynamics]].<ref>{{cite journal \|last1= Mthembu \|first1= L. \|last2= Marwala \|first2= T. \|last3= Friswell \|first3= M.I. \|last4= Adhikari \|first4= S. \|title= Model selection in finite element model updating using the Bayesian evidence statistic \|journal= Mechanical Systems and Signal Processing \|volume= 25 \|issue= 7 \|pages= 2399–2412 \|year= 2011 \|doi=10.1016/j.ymssp.2011.04.001\|bibcode= 2011MSSP...25.2399M }}</ref> This sampling method has also been used in the field of materials modeling. It can be used to learn the [[Partition function (statistical mechanics)\|partition function]] from [[statistical mechanics]] and derive [[thermodynamics\|thermodynamic]] properties. <ref name="partay">{{cite journal\|last1=Partay\|first1=Livia B.\|year=2010\|title=Efficient Sampling of Atomic Configurational Spaces\|journal=The Journal of Physical Chemistry B\|volume=114\|issue=32\|pages=10502–10512\|doi=10.1021/jp1012973\|pmid=20701382\|arxiv=0906.3544\|s2cid=16834142}}</ref>		Since nested sampling was proposed in 2004, it has been used in many aspects of the field of [[astronomy]]. One paper suggested using nested sampling for [[cosmology\|cosmological]] [[model selection]] and object detection, as it "uniquely combines accuracy, general applicability and computational feasibility."<ref name="mukherjee">{{cite journal \|last1= Mukherjee \|first1= P. \|last2= Parkinson \|first2= D. \|last3= Liddle \|first3= A.R. \|title= A Nested Sampling Algorithm for Cosmological Model Selection \|journal= Astrophysical Journal \|volume= 638 \|issue= 2 \|pages= 51–54 \|year= 2006 \|bibcode= 2006ApJ...638L..51M \|doi= 10.1086/501068\|arxiv= astro-ph/0508461\|s2cid= 6208051 }}</ref> A refinement of the algorithm to handle multimodal posteriors has been suggested as a means to detect astronomical objects in extant datasets.<ref name="feroz">{{cite journal \|last1= Feroz \|first1= F. \|last2= Hobson \|first2= M.P. \|title= Multimodal nested sampling: an efficient and robust alternative to Markov Chain Monte Carlo methods for astronomical data analyses \|journal= MNRAS \|volume= 384 \|issue= 2 \|pages= 449–463 \|year= 2008 \|url= http://adsabs.harvard.edu/cgi-bin/bib_query?arXiv:0704.3704 \|doi= 10.1111/j.1365-2966.2007.12353.x \|doi-access= free \|bibcode=2008MNRAS.384..449F \|arxiv= 0704.3704\|s2cid= 14226032 }}</ref> Other applications of nested sampling are in the field of [[finite element updating]] where the algorithm is used to choose an optimal [[finite element]] model, and this was applied to [[structural dynamics]].<ref>{{cite journal \|last1= Mthembu \|first1= L. \|last2= Marwala \|first2= T. \|last3= Friswell \|first3= M.I. \|last4= Adhikari \|first4= S. \|title= Model selection in finite element model updating using the Bayesian evidence statistic \|journal= Mechanical Systems and Signal Processing \|volume= 25 \|issue= 7 \|pages= 2399–2412 \|year= 2011 \|doi=10.1016/j.ymssp.2011.04.001\|bibcode= 2011MSSP...25.2399M }}</ref> This sampling method has also been used in the field of materials modeling. It can be used to learn the [[Partition function (statistical mechanics)\|partition function]] from [[statistical mechanics]] and derive [[thermodynamics\|thermodynamic]] properties. <ref name="partay">{{cite journal\|last1=Partay\|first1=Livia B.\|year=2010\|title=Efficient Sampling of Atomic Configurational Spaces\|journal=The Journal of Physical Chemistry B\|volume=114\|issue=32\|pages=10502–10512\|doi=10.1021/jp1012973\|pmid=20701382\|arxiv=0906.3544\|s2cid=16834142}}</ref>

	==Dynamic nested sampling==		==Dynamic nested sampling==
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	Publicly available dynamic nested sampling software packages include:		Publicly available dynamic nested sampling software packages include:
	* {{Proper name\|dynesty}} - a Python implementation of dynamic nested sampling which can be downloaded from GitHub.<ref>[https://github.com/joshspeagle/dynesty The dynesty nested sampling software package on GitHub]</ref><ref>{{cite journal \|last=Speagle \|first=Joshua \|title=dynesty: A Dynamic Nested Sampling Package for Estimating Bayesian Posteriors and Evidences \|journal=Monthly Notices of the Royal Astronomical Society \|year=2020 \|volume=493 \|issue=3 \|pages=3132–3158 \|doi=10.1093/mnras/staa278 \|arxiv=1904.02180\|s2cid=102354337 }}</ref>		* {{Proper name\|dynesty}} - a Python implementation of dynamic nested sampling which can be downloaded from GitHub.<ref>[https://github.com/joshspeagle/dynesty The dynesty nested sampling software package on GitHub]</ref><ref>{{cite journal \|last=Speagle \|first=Joshua \|title=dynesty: A Dynamic Nested Sampling Package for Estimating Bayesian Posteriors and Evidences \|journal=Monthly Notices of the Royal Astronomical Society \|year=2020 \|volume=493 \|issue=3 \|pages=3132–3158 \|doi=10.1093/mnras/staa278 \|doi-access=free \|arxiv=1904.02180\|s2cid=102354337 }}</ref>
	* dyPolyChord: a software package which can be used with Python, C++ and Fortran likelihood and prior distributions.<ref>{{cite journal \|last1=Higson \|first1=Edward \|title=dyPolyChord: dynamic nested sampling with PolyChord \|journal=Journal of Open Source Software \|date=2018 \|volume=3 \|issue=29 \|page=965 \|doi=10.21105/joss.00965 \|doi-access=free }}</ref> dyPolyChord is available on GitHub.<ref>[https://github.com/ejhigson/dyPolyChord The dyPolyChord dynamic nested sampling software package on GitHub]</ref>		* dyPolyChord: a software package which can be used with Python, C++ and Fortran likelihood and prior distributions.<ref>{{cite journal \|last1=Higson \|first1=Edward \|title=dyPolyChord: dynamic nested sampling with PolyChord \|journal=Journal of Open Source Software \|date=2018 \|volume=3 \|issue=29 \|page=965 \|doi=10.21105/joss.00965 \|doi-access=free }}</ref> dyPolyChord is available on GitHub.<ref>[https://github.com/ejhigson/dyPolyChord The dyPolyChord dynamic nested sampling software package on GitHub]</ref>