Data augmentation for models based on rejection sampling.
Abstract
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.
Type
Journal articleSubject
Bayesian inferenceDensity estimation
Gaussian process
Intractable likelihood
Markov chain Monte Carlo
Matrix Langevin distribution
Rejection sampling
Truncation
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https://hdl.handle.net/10161/15598Published Version (Please cite this version)
10.1093/biomet/asw005Publication Info
Rao, 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.This is constructed from limited available data and may be imprecise. To cite this
article, please review & use the official citation provided by the journal.
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Show full item recordScholars@Duke
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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