A non-asymptotic error analysis for parallel Monte Carlo estimation from many short Markov chains
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866916111266611200 |
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| author | Brown, Austin |
| author_facet | Brown, Austin |
| contents | Single-chain Markov chain Monte Carlo simulates realizations from a Markov chain to estimate expectations with the empirical average. The single-chain simulation is generally of considerable length and restricts many advantages of modern parallel computation. This paper constructs a novel many-short-chains Monte Carlo (MSC) estimator by averaging over multiple independent sums from Markov chains of a guaranteed short length. The computational advantage is the independent Markov chain simulations can be fast and may be run in parallel. The MSC estimator requires an importance sampling proposal and a drift condition on the Markov chain without requiring convergence analysis on the Markov chain. A non-asymptotic error analysis is developed for the MSC estimator under both geometric and multiplicative drift conditions. Empirical performance is illustrated on an autoregressive process and the Pólya-Gamma Gibbs sampler for Bayesian logistic regression to predict cardiovascular disease. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2401_17963 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A non-asymptotic error analysis for parallel Monte Carlo estimation from many short Markov chains Brown, Austin Statistics Theory Computation 60J27, 60J20 Single-chain Markov chain Monte Carlo simulates realizations from a Markov chain to estimate expectations with the empirical average. The single-chain simulation is generally of considerable length and restricts many advantages of modern parallel computation. This paper constructs a novel many-short-chains Monte Carlo (MSC) estimator by averaging over multiple independent sums from Markov chains of a guaranteed short length. The computational advantage is the independent Markov chain simulations can be fast and may be run in parallel. The MSC estimator requires an importance sampling proposal and a drift condition on the Markov chain without requiring convergence analysis on the Markov chain. A non-asymptotic error analysis is developed for the MSC estimator under both geometric and multiplicative drift conditions. Empirical performance is illustrated on an autoregressive process and the Pólya-Gamma Gibbs sampler for Bayesian logistic regression to predict cardiovascular disease. |
| title | A non-asymptotic error analysis for parallel Monte Carlo estimation from many short Markov chains |
| topic | Statistics Theory Computation 60J27, 60J20 |
| url | https://arxiv.org/abs/2401.17963 |