Particle Markov chain Monte Carlo methods
Markov chain Monte Carlo and sequential Monte Carlo methods have emerged as the two main tools to sample from high dimensional probability distributions. Although asymptotic convergence of Markov chain Monte Carlo algorithms is ensured under weak assumptions, the performance of these algorithms is u...
| Main Authors: | , , |
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| Format: | Journal article |
| Language: | English |
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2010
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| _version_ | 1826289107733577728 |
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| author | Andrieu, C Doucet, A Holenstein, R |
| author_facet | Andrieu, C Doucet, A Holenstein, R |
| author_sort | Andrieu, C |
| collection | OXFORD |
| description | Markov chain Monte Carlo and sequential Monte Carlo methods have emerged as the two main tools to sample from high dimensional probability distributions. Although asymptotic convergence of Markov chain Monte Carlo algorithms is ensured under weak assumptions, the performance of these algorithms is unreliable when the proposal distributions that are used to explore the space are poorly chosen and/or if highly correlated variables are updated independently. We show here how it is possible to build efficient high dimensional proposal distributions by using sequential Monte Carlo methods. This allows us not only to improve over standard Markov chain Monte Carlo schemes but also to make Bayesian inference feasible for a large class of statistical models where this was not previously so. We demonstrate these algorithms on a non-linear state space model and a Lévy-driven stochastic volatility model. © 2010 Royal Statistical Society. |
| first_indexed | 2024-03-07T02:23:52Z |
| format | Journal article |
| id | oxford-uuid:a4e8f1c4-db65-4b18-8885-2ac5b3c5b983 |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-07T02:23:52Z |
| publishDate | 2010 |
| record_format | dspace |
| spelling | oxford-uuid:a4e8f1c4-db65-4b18-8885-2ac5b3c5b9832022-03-27T02:36:53ZParticle Markov chain Monte Carlo methodsJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:a4e8f1c4-db65-4b18-8885-2ac5b3c5b983EnglishSymplectic Elements at Oxford2010Andrieu, CDoucet, AHolenstein, RMarkov chain Monte Carlo and sequential Monte Carlo methods have emerged as the two main tools to sample from high dimensional probability distributions. Although asymptotic convergence of Markov chain Monte Carlo algorithms is ensured under weak assumptions, the performance of these algorithms is unreliable when the proposal distributions that are used to explore the space are poorly chosen and/or if highly correlated variables are updated independently. We show here how it is possible to build efficient high dimensional proposal distributions by using sequential Monte Carlo methods. This allows us not only to improve over standard Markov chain Monte Carlo schemes but also to make Bayesian inference feasible for a large class of statistical models where this was not previously so. We demonstrate these algorithms on a non-linear state space model and a Lévy-driven stochastic volatility model. © 2010 Royal Statistical Society. |
| spellingShingle | Andrieu, C Doucet, A Holenstein, R Particle Markov chain Monte Carlo methods |
| title | Particle Markov chain Monte Carlo methods |
| title_full | Particle Markov chain Monte Carlo methods |
| title_fullStr | Particle Markov chain Monte Carlo methods |
| title_full_unstemmed | Particle Markov chain Monte Carlo methods |
| title_short | Particle Markov chain Monte Carlo methods |
| title_sort | particle markov chain monte carlo methods |
| work_keys_str_mv | AT andrieuc particlemarkovchainmontecarlomethods AT douceta particlemarkovchainmontecarlomethods AT holensteinr particlemarkovchainmontecarlomethods |