Data augmentation for models based on rejection sampling.
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We present a data augmentation scheme to perform Markov chain Monte Carlo inference for models where data generation involves a rejection sampling algorithm. Our idea is a simple scheme to instantiate the rejected proposals preceding each data point. The resulting joint probability over observed and rejected variables can be much simpler than the marginal distribution over the observed variables, which often involves intractable integrals. We consider three problems: modelling flow-cytometry measurements subject to truncation; the Bayesian analysis of the matrix Langevin distribution on the Stiefel manifold; and Bayesian inference for a nonparametric Gaussian process density model. The latter two are instances of doubly-intractable Markov chain Monte Carlo problems, where evaluating the likelihood is intractable. Our experiments demonstrate superior performance over state-of-the-art sampling algorithms for such problems.
Markov chain Monte Carlo
Matrix Langevin distribution
Published Version (Please cite this version)10.1093/biomet/asw005
Publication InfoRao, Vinayak; Lin, Lizhen; & Dunson, David B (2016). Data augmentation for models based on rejection sampling. Biometrika, 103(2). pp. 319-335. 10.1093/biomet/asw005. Retrieved from https://hdl.handle.net/10161/15598.
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Arts and Sciences Distinguished Professor of Statistical Science
Development of novel approaches for representing and analyzing complex data. A particular focus is on methods that incorporate geometric structure (both known and unknown) and on probabilistic approaches to characterize uncertainty. In addition, a big interest is in scalable algorithms and in developing approaches with provable guarantees.This fundamental work is directly motivated by applications in biomedical research, network data analysis, neuroscience, genomics, ecol