A0637
Title: Bayesian inference via predictive distributions
Authors: Samuele Garelli - University of Bologna (Italy) [presenting]
Abstract: Predictive distributions offer an appealing alternative to the likelihood-prior-posterior approach to Bayesian inference. In fact, if predictive distributions have a good fit on the observed data and converge in some sense, they can be used to perform inference. Moreover, choosing $P(X_{n+1} | X_1,...,X_n)$ is more natural than specifying a prior distribution since the former is defined on the data (i.e. observables) while the latter is defined on parameters (i.e. unobservables). In practice, inference can be carried out by reconstructing the unobserved part of the population via recursive sampling from the predictive distributions and by taking statistics of the observed and the imputed data together. A way to define predictive distributions that are both theoretically and computationally tractable is via mixtures of distributions initialized by a clustering algorithm whose dynamics are driven by the mean and the variance of each cluster. Such predictive distributions enjoy interesting convergence properties and can be used to target three main inferential tasks, i.e. parameter estimation, regression and classification.
