Scalable Bernoulli factories for Bayesian inference with intractable likelihoods
Fuente:
arXiv
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866911060998488064 |
|---|---|
| author | Stumpf-Fétizon, Timothée Gonçalves, Flávio B. |
| author_facet | Stumpf-Fétizon, Timothée Gonçalves, Flávio B. |
| contents | Bernoulli factory MCMC algorithms implement accept-reject Markov chains without explicit computation of acceptance probabilities, and are used to target posterior distributions associated with intractable likelihood models. Intractable likelihoods naturally arise in continuous-time models and mixture distributions, or from the marginalisation of a tractable augmented model. Bernoulli factory MCMC algorithms often mix better than alternatives that target a tractable augmented posterior. However, for a likelihood that factorizes over observations, we show that their computational performance typically deteriorates exponentially with data size. To address this, we propose a simple divide-and-conquer Bernoulli factory MCMC algorithm and prove that it has polynomial complexity of degree between 1 and 2, with the exact degree depending on the existence of efficient unbiased estimators of the intractable likelihood ratio. We demonstrate the effectiveness of our approach with applications to Bayesian inference in two intractable likelihood models, and observe respective polynomial cost of degree 1.2 and 1 in the data size. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_05438 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Scalable Bernoulli factories for Bayesian inference with intractable likelihoods Stumpf-Fétizon, Timothée Gonçalves, Flávio B. Computation 62-08 G.3 Bernoulli factory MCMC algorithms implement accept-reject Markov chains without explicit computation of acceptance probabilities, and are used to target posterior distributions associated with intractable likelihood models. Intractable likelihoods naturally arise in continuous-time models and mixture distributions, or from the marginalisation of a tractable augmented model. Bernoulli factory MCMC algorithms often mix better than alternatives that target a tractable augmented posterior. However, for a likelihood that factorizes over observations, we show that their computational performance typically deteriorates exponentially with data size. To address this, we propose a simple divide-and-conquer Bernoulli factory MCMC algorithm and prove that it has polynomial complexity of degree between 1 and 2, with the exact degree depending on the existence of efficient unbiased estimators of the intractable likelihood ratio. We demonstrate the effectiveness of our approach with applications to Bayesian inference in two intractable likelihood models, and observe respective polynomial cost of degree 1.2 and 1 in the data size. |
| title | Scalable Bernoulli factories for Bayesian inference with intractable likelihoods |
| topic | Computation 62-08 G.3 |
| url | https://arxiv.org/abs/2505.05438 |