In this talk, Bayesian semiparametric methods for function estimation and model selection problems are presented. This talk is designed to provide graduate students and researchers with an introduction to Bayesian semiparametric inference. The orientation is methodological rather than theoretical, but such asymptotic theory as is necessary for a proper understanding and validating specific Bayesian methods will be also covered in detail. The materials will include three aspects of Bayesian inference, (i) Fundamentals (ii) Asymptotics and (iii) Advanced models, focusing on nonparametric and semiparametric methods. For function estimation, the Bayesian semiparametric models using Gaussian process priors are discussed. For model selection, Bayes factors are explained for dealing with lack of fit in regression and goodness of fit in density estimation problems.

In this talk, Bayesian semiparametric methods for function estimation and model selection problems are presented. This talk is designed to provide graduate students and researchers with an introduction to Bayesian semiparametric inference. The orientation is methodological rather than theoretical, but such asymptotic theory as is necessary for a proper understanding and validating specific Bayesian methods will be also covered in detail. The materials will include three aspects of Bayesian inference, (i) Fundamentals (ii) Asymptotics and (iii) Advanced models, focusing on nonparametric and semiparametric methods. For function estimation, the Bayesian semiparametric models using Gaussian process priors are discussed. For model selection, Bayes factors are explained for dealing with lack of fit in regression and goodness of fit in density estimation problems.