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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David B. Dunson
Arts and Sciences Distinguished Professor of Statistical Science
My research focuses on developing new tools for probabilistic learning from complex data - methods development is directly motivated by challenging applications in ecology/biodiversity, neuroscience, environmental health, criminal justice/fairness, and more. We seek to develop new modeling frameworks, algorithms and corresponding code that can be used routinely by scientists and decision makers. We are also interested in new inference framework and in studying theoretical properties
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