Priors over related distributions have received increased attention in the Bayesian literature. Recent papers include De Iorio, Mueller, Rosner, and MacEachern (2004), Gelfand, Kottas, and MacEachern (2005), Griffin and Steel (2006), Dunson, Pillai, and Park (2007), Dunson (2007), Reich and Fuentes (2007), Dunson and Park (2008), and many others. All of these approaches generalize some aspect of a stick-breaking prior, either by including weights that change with covariate levels (which could be time or space), atoms that change with covariate levels, or both. These processes are typically convolved with a continuous, usually normal kernel yielding a smooth density at each covariate level.
In this talk I will discuss some alternative nonparametric dependent
processes: tailfree priors where conditional probabilities are
stochastic processes or simple parametric functions indexed by
covariates. Fixing the partition across covariate levels simplifies
computations and allows analyses of rather large, censored data sets.
Data applications include a generalization of the accelerated failure
time model where parameters retain interpretability in terms of median
survival, an example of growth curve analyses, and a Rasch model
applied to educational testing data where the student-specific random
effects distribution changes with levels of covariates.
Meet the speaker in Room 212 Cockins Hall at 4:30 p.m. Refreshments will be served.