Semiparametric Bayes Joint Modeling with Functional Predictors

We consider the problem of semiparametric Bayes joint modeling of predictors and a response variable, with a particular emphasis on functional predictors. Parametric models for the predictor and response are coupled through a joint distribution for subjectspecific predictor and response coefficients. This joint distribution is assigned a flexible mixture prior, which allows the response distribution within predictor clusters to be unknown. Marginalizing out the random atoms and random weights, we obtain a useful closed form bivariate predictor rule. To avoid label ambiguity and accelerate computation, we propose a combined sequential updating and Gibbs sampling algorithm for posterior computation. The methods are applied to data on weight gain during pregnancy and birth weight.