Gespeichert in:
| Hauptverfasser: | , , , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2024
|
| Schlagworte: | |
| Online-Zugang: | https://arxiv.org/abs/2407.12608 |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866913891297001472 |
|---|---|
| author | Heiner, Matthew J. Johnson, Samuel B. Christensen, Joshua R. Dahl, David B. |
| author_facet | Heiner, Matthew J. Johnson, Samuel B. Christensen, Joshua R. Dahl, David B. |
| contents | We propose and demonstrate a novel, effective approach to slice sampling. Using the probability integral transform, we first generalize Neal's shrinkage algorithm, standardizing the procedure to an automatic and universal starting point: the unit interval. This enables the introduction of approximate (pseudo-) targets through the factorization used in importance sampling, a technique that popularized elliptical slice sampling, while still sampling from the correct target distribution. Accurate pseudo-targets can boost sampler efficiency by requiring fewer rejections and by reducing skewness in the transformed target. This strategy is effective when a natural, possibly crude approximation to the target exists. Alternatively, obtaining a marginal pseudo-target from initial samples provides an intuitive and automatic tuning procedure. We consider two metrics for evaluating the quality of approximation; each can be used as a criterion to find an optimal pseudo-target or as an interpretable diagnostic. We examine performance of the proposed sampler relative to other popular, easily implemented MCMC samplers on standard targets in isolation, and as steps within a Gibbs sampler in a Bayesian modeling context. We extend the transformation method to multivariate slice samplers and demonstrate with a constrained state-space model for which a readily available forward-backward algorithm provides the target approximation. Supplemental materials and accompanying R package qslice are available online. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_12608 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Quantile Slice Sampling Heiner, Matthew J. Johnson, Samuel B. Christensen, Joshua R. Dahl, David B. Computation We propose and demonstrate a novel, effective approach to slice sampling. Using the probability integral transform, we first generalize Neal's shrinkage algorithm, standardizing the procedure to an automatic and universal starting point: the unit interval. This enables the introduction of approximate (pseudo-) targets through the factorization used in importance sampling, a technique that popularized elliptical slice sampling, while still sampling from the correct target distribution. Accurate pseudo-targets can boost sampler efficiency by requiring fewer rejections and by reducing skewness in the transformed target. This strategy is effective when a natural, possibly crude approximation to the target exists. Alternatively, obtaining a marginal pseudo-target from initial samples provides an intuitive and automatic tuning procedure. We consider two metrics for evaluating the quality of approximation; each can be used as a criterion to find an optimal pseudo-target or as an interpretable diagnostic. We examine performance of the proposed sampler relative to other popular, easily implemented MCMC samplers on standard targets in isolation, and as steps within a Gibbs sampler in a Bayesian modeling context. We extend the transformation method to multivariate slice samplers and demonstrate with a constrained state-space model for which a readily available forward-backward algorithm provides the target approximation. Supplemental materials and accompanying R package qslice are available online. |
| title | Quantile Slice Sampling |
| topic | Computation |
| url | https://arxiv.org/abs/2407.12608 |