MCMC Sampling and Bayesian Inference, Views and News
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Where
Title: MCMC Sampling and Bayesian Inference, Views and News
Abstract:
Bayesian inference is a philosophical framework for learning from data.
In many practical applications, the technical difficulty is sampling from
the posterior distribution using Markov Chain Monte Carlo (MCMC). A sampler
is an algorithm that creates random parameter sets from the posterior, using
a simple random number generator.
I will describe some personal views, including difficulties in constructing
good samplers and practical measures of sampling quality. I discuss the class
of affine invariant ensemble samplers including a newly proposed variant.
Results will be presented for the problem of learning parameters that describe
the system of chemical reactions involved in hydrogen flames. I discuss the
distinction between uncertainty quantification (how well the parameters are
determined) and uncertainty propagation (how uncertainties matter).
I describe samplers for distributions with hard or soft constraints. Hard
constraints restrict the distribution to embedded surfaces. Soft constraints
give distributions concentrated near such surfaces.
Several theoretical and practical open problems will be described.
Refreshments will be served in the Math Commons Room at 3:30pm