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Abstract:
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To improve the efficiency of Monte Carlo estimation, practitioners are turning to biased Markov chain Monte Carlo procedures that trade off asymptotic exactness for computational speed. The reasoning is sound: a reduction in variance due to more rapid sampling can outweigh the bias introduced. However, the inexactness creates new challenges for sampler and parameter selection, since standard measures of sample quality like effective sample size do not account for asymptotic bias. To address these challenges, we introduce new computable quality measures based onStein's method that quantify the maximum discrepancy between sample and target expectations over a large class of test functions. We use our tools to compare exact, biased, and deterministicsample sequences and illustrate applications to hyperparameter selection, biased sampler selection, one-sample hypothesis testing, and sample quality improvement.
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