Applied Bayes/Comp Stats seminar Monday 11th Sept
Geoff Nicholls
Hi folks,
Dennis Christensen will give a talk next week on Monday 11th September. He is a PhD student in the
Statistics and Data Science group at UIO, supervised by Nils Hjort and Erik Unneberg.
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Time: Monday 11th September 2-3pm
Place: SLT3, Department of Statistics
Speaker: Dennis Christensen (UIO)
Title : A symmetry-based simulation method for Bayesian nonparametric models with binary response data
Abstract: Binary responses are a central object of study in statistics, and arise naturally in applica tions such as bioassay, current-status data and sensitivity testing. There has been a large interest in applying Bayesian nonparametric models to such data since the early 1970s. For models based on Dirichlet processes, posterior inference is possible via Markov chain Monte Carlo (MCMC) methods. However, for many modern model choices, such MCMC based methods fail. Here we present a new importance sampling algorithm for nonparametric models given exchangeable binary response data. Unlike approximate methods, this algorithm converges to the true posterior distribution, and also yields a consistent estimator for the marginal likelihood. It can be applied to any model from which samples can be generated, or even approximately generated. The main idea behind the algorithm is to exploit the symmetries introduced by exchangeability of the data, and then to correct for this exploitation by multiplying by an appropriate importance weight. Calculating the weights turns out to be equivalent to evaluating the permanents of a certain class of 0-1 matrices, which we prove can be done in polynomial time by deriving an explicit algorithm. We apply the new technique to both synthetic and real data.
Paper: “Inference for Bayesian Nonparametric Models with Binary Response Data via Permutation Counting”,
Dennis Christensen, Bayesian Anal. Advance Publication 1-26 (2022). DOI: 10.1214/22-BA1353
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Best,
Geoff
Prof Geoff Nicholls
Associate Professor of Statistics, University of Oxford
Fellow and Tutor in Statistics, St Peter’s college
Geoff Nicholls
Today at 2pm. Best, Geoff