Noisy Monte Carlo: convergence of Markov chains with approximate transition kernels
Abstract Monte Carlo algorithms often aim to draw from a distribution $$\pi $$ by simulating a Markov chain with transition kernel $$P$$ such that $$\pi $$ is invariant under $$P$$. However, there are many situations for which it is impractical or impossible to draw from the transition kernel $$P$$....
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| Autor*in: |
Alquier, P. [verfasserIn] |
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Artikel |
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| Sprache: |
Englisch |
| Erschienen: |
2014 |
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| Schlagwörter: |
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| Anmerkung: |
© Springer Science+Business Media New York 2014 |
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| Übergeordnetes Werk: |
Enthalten in: Statistics and computing - Springer US, 1991, 26(2014), 1-2 vom: 10. Dez., Seite 29-47 |
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| Übergeordnetes Werk: |
volume:26 ; year:2014 ; number:1-2 ; day:10 ; month:12 ; pages:29-47 |
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10.1007/s11222-014-9521-x |
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| 520 | |a Abstract Monte Carlo algorithms often aim to draw from a distribution $$\pi $$ by simulating a Markov chain with transition kernel $$P$$ such that $$\pi $$ is invariant under $$P$$. However, there are many situations for which it is impractical or impossible to draw from the transition kernel $$P$$. For instance, this is the case with massive datasets, where is it prohibitively expensive to calculate the likelihood and is also the case for intractable likelihood models arising from, for example, Gibbs random fields, such as those found in spatial statistics and network analysis. A natural approach in these cases is to replace $$P$$ by an approximation $$\hat{P}$$. Using theory from the stability of Markov chains we explore a variety of situations where it is possible to quantify how ‘close’ the chain given by the transition kernel $$\hat{P}$$ is to the chain given by $$P$$. We apply these results to several examples from spatial statistics and network analysis. | ||
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10.1007/s11222-014-9521-x doi (DE-627)OLC203374793X (DE-He213)s11222-014-9521-x-p DE-627 ger DE-627 rakwb eng 004 620 VZ Alquier, P. verfasserin aut Noisy Monte Carlo: convergence of Markov chains with approximate transition kernels 2014 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer Science+Business Media New York 2014 Abstract Monte Carlo algorithms often aim to draw from a distribution $$\pi $$ by simulating a Markov chain with transition kernel $$P$$ such that $$\pi $$ is invariant under $$P$$. However, there are many situations for which it is impractical or impossible to draw from the transition kernel $$P$$. For instance, this is the case with massive datasets, where is it prohibitively expensive to calculate the likelihood and is also the case for intractable likelihood models arising from, for example, Gibbs random fields, such as those found in spatial statistics and network analysis. A natural approach in these cases is to replace $$P$$ by an approximation $$\hat{P}$$. Using theory from the stability of Markov chains we explore a variety of situations where it is possible to quantify how ‘close’ the chain given by the transition kernel $$\hat{P}$$ is to the chain given by $$P$$. We apply these results to several examples from spatial statistics and network analysis. Markov chain Monte Carlo Pseudo-marginal Monte Carlo Intractable likelihoods Friel, N. aut Everitt, R. aut Boland, A. aut Enthalten in Statistics and computing Springer US, 1991 26(2014), 1-2 vom: 10. Dez., Seite 29-47 (DE-627)131007963 (DE-600)1087487-2 (DE-576)052732894 0960-3174 nnns volume:26 year:2014 number:1-2 day:10 month:12 pages:29-47 https://doi.org/10.1007/s11222-014-9521-x lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-TEC SSG-OLC-MAT GBV_ILN_70 GBV_ILN_2012 GBV_ILN_4126 AR 26 2014 1-2 10 12 29-47 |
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10.1007/s11222-014-9521-x doi (DE-627)OLC203374793X (DE-He213)s11222-014-9521-x-p DE-627 ger DE-627 rakwb eng 004 620 VZ Alquier, P. verfasserin aut Noisy Monte Carlo: convergence of Markov chains with approximate transition kernels 2014 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer Science+Business Media New York 2014 Abstract Monte Carlo algorithms often aim to draw from a distribution $$\pi $$ by simulating a Markov chain with transition kernel $$P$$ such that $$\pi $$ is invariant under $$P$$. However, there are many situations for which it is impractical or impossible to draw from the transition kernel $$P$$. For instance, this is the case with massive datasets, where is it prohibitively expensive to calculate the likelihood and is also the case for intractable likelihood models arising from, for example, Gibbs random fields, such as those found in spatial statistics and network analysis. A natural approach in these cases is to replace $$P$$ by an approximation $$\hat{P}$$. Using theory from the stability of Markov chains we explore a variety of situations where it is possible to quantify how ‘close’ the chain given by the transition kernel $$\hat{P}$$ is to the chain given by $$P$$. We apply these results to several examples from spatial statistics and network analysis. Markov chain Monte Carlo Pseudo-marginal Monte Carlo Intractable likelihoods Friel, N. aut Everitt, R. aut Boland, A. aut Enthalten in Statistics and computing Springer US, 1991 26(2014), 1-2 vom: 10. Dez., Seite 29-47 (DE-627)131007963 (DE-600)1087487-2 (DE-576)052732894 0960-3174 nnns volume:26 year:2014 number:1-2 day:10 month:12 pages:29-47 https://doi.org/10.1007/s11222-014-9521-x lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-TEC SSG-OLC-MAT GBV_ILN_70 GBV_ILN_2012 GBV_ILN_4126 AR 26 2014 1-2 10 12 29-47 |
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Noisy Monte Carlo: convergence of Markov chains with approximate transition kernels |
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Abstract Monte Carlo algorithms often aim to draw from a distribution $$\pi $$ by simulating a Markov chain with transition kernel $$P$$ such that $$\pi $$ is invariant under $$P$$. However, there are many situations for which it is impractical or impossible to draw from the transition kernel $$P$$. For instance, this is the case with massive datasets, where is it prohibitively expensive to calculate the likelihood and is also the case for intractable likelihood models arising from, for example, Gibbs random fields, such as those found in spatial statistics and network analysis. A natural approach in these cases is to replace $$P$$ by an approximation $$\hat{P}$$. Using theory from the stability of Markov chains we explore a variety of situations where it is possible to quantify how ‘close’ the chain given by the transition kernel $$\hat{P}$$ is to the chain given by $$P$$. We apply these results to several examples from spatial statistics and network analysis. © Springer Science+Business Media New York 2014 |
| abstractGer |
Abstract Monte Carlo algorithms often aim to draw from a distribution $$\pi $$ by simulating a Markov chain with transition kernel $$P$$ such that $$\pi $$ is invariant under $$P$$. However, there are many situations for which it is impractical or impossible to draw from the transition kernel $$P$$. For instance, this is the case with massive datasets, where is it prohibitively expensive to calculate the likelihood and is also the case for intractable likelihood models arising from, for example, Gibbs random fields, such as those found in spatial statistics and network analysis. A natural approach in these cases is to replace $$P$$ by an approximation $$\hat{P}$$. Using theory from the stability of Markov chains we explore a variety of situations where it is possible to quantify how ‘close’ the chain given by the transition kernel $$\hat{P}$$ is to the chain given by $$P$$. We apply these results to several examples from spatial statistics and network analysis. © Springer Science+Business Media New York 2014 |
| abstract_unstemmed |
Abstract Monte Carlo algorithms often aim to draw from a distribution $$\pi $$ by simulating a Markov chain with transition kernel $$P$$ such that $$\pi $$ is invariant under $$P$$. However, there are many situations for which it is impractical or impossible to draw from the transition kernel $$P$$. For instance, this is the case with massive datasets, where is it prohibitively expensive to calculate the likelihood and is also the case for intractable likelihood models arising from, for example, Gibbs random fields, such as those found in spatial statistics and network analysis. A natural approach in these cases is to replace $$P$$ by an approximation $$\hat{P}$$. Using theory from the stability of Markov chains we explore a variety of situations where it is possible to quantify how ‘close’ the chain given by the transition kernel $$\hat{P}$$ is to the chain given by $$P$$. We apply these results to several examples from spatial statistics and network analysis. © Springer Science+Business Media New York 2014 |
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| title_short |
Noisy Monte Carlo: convergence of Markov chains with approximate transition kernels |
| url |
https://doi.org/10.1007/s11222-014-9521-x |
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false |
| author2 |
Friel, N. Everitt, R. Boland, A. |
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Friel, N. Everitt, R. Boland, A. |
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131007963 |
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| doi_str |
10.1007/s11222-014-9521-x |
| up_date |
2024-07-03T18:17:13.150Z |
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1803582841187991552 |
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