Scalable importance tempering and Bayesian variable selection
We propose a Monte Carlo algorithm to sample from high dimensional probability distributions that combines Markov chain Monte Carlo and importance sampling. We provide a careful theoretical analysis, including guarantees on robustness to high dimensionality, explicit comparison with standard Markov...
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| Vydané v: | Journal of the Royal Statistical Society. Series B, Statistical methodology Ročník 81; číslo 3; s. 489 - 517 |
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| Hlavní autori: | , |
| Médium: | Journal Article |
| Jazyk: | English |
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Oxford
Wiley
01.07.2019
Oxford University Press |
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| ISSN: | 1369-7412, 1467-9868 |
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| Abstract | We propose a Monte Carlo algorithm to sample from high dimensional probability distributions that combines Markov chain Monte Carlo and importance sampling. We provide a careful theoretical analysis, including guarantees on robustness to high dimensionality, explicit comparison with standard Markov chain Monte Carlo methods and illustrations of the potential improvements in efficiency. Simple and concrete intuition is provided for when the novel scheme is expected to outperform standard schemes. When applied to Bayesian variable-selection problems, the novel algorithm is orders of magnitude more efficient than available alternative sampling schemes and enables fast and reliable fully Bayesian inferences with tens of thousand regressors. |
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| AbstractList | We propose a Monte Carlo algorithm to sample from high dimensional probability distributions that combines Markov chain Monte Carlo and importance sampling. We provide a careful theoretical analysis, including guarantees on robustness to high dimensionality, explicit comparison with standard Markov chain Monte Carlo methods and illustrations of the potential improvements in efficiency. Simple and concrete intuition is provided for when the novel scheme is expected to outperform standard schemes. When applied to Bayesian variable-selection problems, the novel algorithm is orders of magnitude more efficient than available alternative sampling schemes and enables fast and reliable fully Bayesian inferences with tens of thousand regressors. Summary We propose a Monte Carlo algorithm to sample from high dimensional probability distributions that combines Markov chain Monte Carlo and importance sampling. We provide a careful theoretical analysis, including guarantees on robustness to high dimensionality, explicit comparison with standard Markov chain Monte Carlo methods and illustrations of the potential improvements in efficiency. Simple and concrete intuition is provided for when the novel scheme is expected to outperform standard schemes. When applied to Bayesian variable‐selection problems, the novel algorithm is orders of magnitude more efficient than available alternative sampling schemes and enables fast and reliable fully Bayesian inferences with tens of thousand regressors. |
| Author | Zanella, Giacomo Roberts, Gareth |
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| Cites_doi | 10.1007/s11222-008-9108-5 10.1093/biomet/83.3.681 10.1016/0304-4149(94)90134-1 10.1111/1467-9469.00250 10.1080/01621459.2016.1222288 10.1111/1467-9868.00070 10.1214/15-AOS1417 10.1198/016214503388619193 10.1080/01621459.2017.1371025 10.1016/S0304-4076(00)00076-2 10.5539/ijsp.v5n1p51 10.1017/jpr.2016.9 10.1080/01621459.2015.1130634 10.1016/0304-4076(95)01763-1 10.1209/0295-5075/19/6/002 10.1007/978-1-4471-3267-7 10.1214/10-AOAS377 10.1080/01621459.2019.1585255 10.1214/08-AOS634 10.1093/biomet/82.3.479 10.1016/j.ccr.2012.08.013 10.1214/17-AAP1358 10.1080/01621459.2012.682536 10.1080/01621459.1995.10476590 |
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| SubjectTerms | Algorithms Bayesian analysis Bayesian theory Bayesian variable selection; Computational complexity; Gibbs sampling; Importance sampling; Markov chain Monte Carlo sampling; Point mass priors concrete equations Importance sampling Intuition Markov analysis Markov chain Markov chains Monte Carlo method Monte Carlo simulation probability distribution Regression analysis Robustness Sampling Statistical methods Statistics tempering |
| Title | Scalable importance tempering and Bayesian variable selection |
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