Statistics Seminars: The effect of prior-data conflict in Bayesian linear regression
14 April 2010 11:45 in Department of Mathematical Sciences, Durham University
Prior-data conflict appears in Bayesian analysis if the observed data are very unlikely with respect to the prior model and the sample size is not large enough to eliminate the influence of the prior. Prior-data conflict is often not reflected in posterior inferences. We consider Bayesian linear regression models based on conjugate priors, and demonstrate that a standard prior model may show some reaction to prior-data conflict. A restricted version of this prior, derived via a general construction procedure for exponential family sampling models, offers clearer insight in some aspects of the update process and is well suited for a generalization towards an imprecise probability model, where, by considering sets of prior distributions instead of a single prior, prior-data conflict can be handled in an appealing and intuitive way. (joint work with T. Augustin, University of Munich).
An event within the Lecture Day with Prof. Balakrishnan, more info available at http://www.maths.dur.ac.uk/~dma0je/bala/