Bayesian Latent Variable Methods with Some Applications

• Activity Number: 458
• Type: Topic Contributed
• Date/Time: Wednesday, August 3, 2011 : 8:30 AM to 10:20 AM
• Sponsor: Section on Bayesian Statistical Science
• Author(s): Saman Muthukumarana*+ and Tim Swartz
• Companies: University of Manitoba and Simon Fraser University
• Keywords: Latent variables ; Goodness-of-fit ; MCMC

Abstract

In Bayesian statistics we are interested in the posterior distribution of parameters. In simple cases we can derive analytical expressions for the posterior. However in most situations, the posterior expectations cannot be calculated analytically in the existence of latent variables, multidimensional parameters, and complex model structures. When the resulting posterior distribution is complex and high-dimensional, posterior expectations can be approximated by MCMC methods. In this talk, I will present how Bayesian latent variable methods can be developed in diverse problems in the fields of sports, network and ordinal survey data. The proposed methodologies are tested through simulation studies. Goodness-of-fit procedures are also discussed for assessing the validity of the methods. In our applications, the data are high dimensional, and we advocate a comparison of prior-predictive output versus observed data via "features" using Euclidean distances. Goodness-of-fit procedures based on pivotal quantities are also discussed. The proposed goodness-of-fit procedures are intuitive and flexible in the sense that one can investigate features which are relevant to the particular model.