Pseudo-Marginal Slice Sampling

Iain Murray, Matthew Graham
Proceedings of the 19th International Conference on Artificial Intelligence and Statistics, PMLR 51:911-919, 2016.

Abstract

Markov chain Monte Carlo (MCMC) methods asymptotically sample from complex probability distributions. The pseudo-marginal MCMC framework only requires an unbiased estimator of the unnormalized probability distribution function to construct a Markov chain. However, the resulting chains are harder to tune to a target distribution than conventional MCMC, and the types of updates available are limited. We describe a general way to clamp and update the random numbers used in a pseudo-marginal method’s unbiased estimator. In this framework we can use slice sampling and other adaptive methods. We obtain more robust Markov chains, which often mix more quickly.

Cite this Paper

BibTeX
@InProceedings{pmlr-v51-murray16, title = {Pseudo-Marginal Slice Sampling}, author = {Murray, Iain and Graham, Matthew}, booktitle = {Proceedings of the 19th International Conference on Artificial Intelligence and Statistics}, pages = {911--919}, year = {2016}, editor = {Gretton, Arthur and Robert, Christian C.}, volume = {51}, series = {Proceedings of Machine Learning Research}, address = {Cadiz, Spain}, month = {09--11 May}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v51/murray16.pdf}, url = {https://proceedings.mlr.press/v51/murray16.html}, abstract = {Markov chain Monte Carlo (MCMC) methods asymptotically sample from complex probability distributions. The pseudo-marginal MCMC framework only requires an unbiased estimator of the unnormalized probability distribution function to construct a Markov chain. However, the resulting chains are harder to tune to a target distribution than conventional MCMC, and the types of updates available are limited. We describe a general way to clamp and update the random numbers used in a pseudo-marginal method’s unbiased estimator. In this framework we can use slice sampling and other adaptive methods. We obtain more robust Markov chains, which often mix more quickly.} }
Endnote
%0 Conference Paper %T Pseudo-Marginal Slice Sampling %A Iain Murray %A Matthew Graham %B Proceedings of the 19th International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2016 %E Arthur Gretton %E Christian C. Robert %F pmlr-v51-murray16 %I PMLR %P 911--919 %U https://proceedings.mlr.press/v51/murray16.html %V 51 %X Markov chain Monte Carlo (MCMC) methods asymptotically sample from complex probability distributions. The pseudo-marginal MCMC framework only requires an unbiased estimator of the unnormalized probability distribution function to construct a Markov chain. However, the resulting chains are harder to tune to a target distribution than conventional MCMC, and the types of updates available are limited. We describe a general way to clamp and update the random numbers used in a pseudo-marginal method’s unbiased estimator. In this framework we can use slice sampling and other adaptive methods. We obtain more robust Markov chains, which often mix more quickly.
RIS
TY - CPAPER TI - Pseudo-Marginal Slice Sampling AU - Iain Murray AU - Matthew Graham BT - Proceedings of the 19th International Conference on Artificial Intelligence and Statistics DA - 2016/05/02 ED - Arthur Gretton ED - Christian C. Robert ID - pmlr-v51-murray16 PB - PMLR DP - Proceedings of Machine Learning Research VL - 51 SP - 911 EP - 919 L1 - http://proceedings.mlr.press/v51/murray16.pdf UR - https://proceedings.mlr.press/v51/murray16.html AB - Markov chain Monte Carlo (MCMC) methods asymptotically sample from complex probability distributions. The pseudo-marginal MCMC framework only requires an unbiased estimator of the unnormalized probability distribution function to construct a Markov chain. However, the resulting chains are harder to tune to a target distribution than conventional MCMC, and the types of updates available are limited. We describe a general way to clamp and update the random numbers used in a pseudo-marginal method’s unbiased estimator. In this framework we can use slice sampling and other adaptive methods. We obtain more robust Markov chains, which often mix more quickly. ER -
APA
Murray, I. & Graham, M.. (2016). Pseudo-Marginal Slice Sampling. Proceedings of the 19th International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 51:911-919 Available from https://proceedings.mlr.press/v51/murray16.html.

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