The Bayesian paradigm for statistical inference uses expert knowledge, formulated in terms of probability distributions of unknown parameters of interest. These distributions, called prior distributions, are combined with data to provide new information about parameters, via new parameter distributions called posterior distributions. One research theme centers on devising new Bayesian methodologies, i.e., new statistical models with which Bayesian inferences can provide particular scientific insight. Quantifying the statistical properties of such methods and contrasting with non-Bayesian alternatives is an active area of research. Bayesian methods can lead to computational challenges, and another research theme centers on efficient computation of Bayesian solutions. The development of computational techniques for determining posterior distributions, such as Monte Carlo methods, is a rich area of research activity, with particular emphasis on Markov Chain Monte Carlo methods and sequential Monte Carlo methods.
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