Data augmentation for models based on rejection sampling.

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2016-06

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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.

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10.1093/biomet/asw005

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Rao, Vinayak, Lizhen Lin and David B Dunson (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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Dunson

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 of methods we develop.  

Some highlight application areas: 
(1) Modeling of biological communities and biodiversity - we are considering global data on fungi, insects, birds and animals including DNA sequences, images, audio, etc.  Data contain large numbers of species unknown to science and we would like to learn about these new species, community network structure, and the impact of environmental change and climate.

(2) Brain connectomics - based on high resolution imaging data of the human brain, we are seeking to developing new statistical and machine learning models for relating brain networks to human traits and diseases.

(3) Environmental health & mixtures - we are building tools for relating chemical and other exposures (air pollution etc) to human health outcomes, accounting for spatial dependence in both exposures and disease.  This includes an emphasis on infectious disease modeling, such as COVID-19.

Some statistical areas that play a prominent role in our methods development include models for low-dimensional structure in data (latent factors, clustering, geometric and manifold learning), flexible/nonparametric models (neural networks, Gaussian/spatial processes, other stochastic processes), Bayesian inference frameworks, efficient sampling and analytic approximation algorithms, and models for "object data" (trees, networks, images, spatial processes, etc).





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