General Departmental Seminar Series
A Bayesian Chi-Squared Test for Goodness-of-Fit
Valen Johnson, PhD, Dept. of Biostatistics, University of Michigan
Friday, October 10, 2003, 12:00 - 1:00 p.m.
G5/136-142 Clinical Sciences Center, 600 Highland Ave.
In this talk I describe an extension of classical Chi-Squared goodness-of-fit tests to Bayesian model assessment. The extension, which essentially involves evaluating Pearson's goodness-of-fit statistic at a parameter value drawn from its posterior distribution, has the important property that it is asymptotically distributed as a Chi-Squared random variable on (number of bins)-1 degrees of freedom, independently of the dimension of the underlying parameter vector. By averaging over the posterior distribution of this statistic, a global goodness-of-fit diagnostic is obtained. Advantages of this diagnostic--which may be interpreted as the area under an ROC curve--include ease of interpretation, computational convenience, and favorable power properties. The proposed diagnostic can be used to assess the adequacy of a broad class of Bayesian models, essentially requiring only a finite-dimensional parameter vector and conditionally independent observations.