Measuring sample quality with diffusions

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• Sebastian Vollmer (Oxford)
• Friday 25 November 2016, 16:00-17:00
• MR12, Centre for Mathematical Sciences, Wilberforce Road, Cambridge..

If you have a question about this talk, please contact Quentin Berthet.

Standard Markov chain Monte Carlo diagnostics, like effective sample size, are ineffective for biased sampling procedures that sacrifice asymptotic correctness for computational speed. Recent work addresses this issue for a class of strongly log-concave target distributions by constructing a computable discrepancy measure based on Stein’s method that provably determines convergence to the target. We generalize this approach to cover any target with a fast-coupling Ito diffusion by bounding the derivatives of Stein equation solutions in terms of Markov process coupling rates. As example applications, we develop computable and convergence-determining diffusion Stein discrepancies for log-concave, heavy-tailed, and multimodal targets and use these quality measures to select the hyperparameters of biased samplers, compare random and deterministic quadrature rules, and quantify bias-variance tradeoffs in approximate Markov chain Monte Carlo. Our explicit multivariate Stein factor bounds may be of independent interest. Preprint: https://arxiv.org/abs/1611.06972

This talk is part of the Statistics series.

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