Mathematical Sciences: Bayesian Inference for Nonparametric Regression in Generalized Linear Models

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9410984 Raghavan The focus of this proposal is the modeling of the functional dependence of non-Gaussian response variables on a given set of predictors. Examples of this include the logistic regression model, where the response is binary and the log-linear Poisson model where the response represents counts of incidents in a given time interval. The function of interest is estimated nonparametrically, using generalized smoothing splines. Inferential procedures based on a Bayesian formulation, wherein a stochastic process prior is imposed on this function, will be investigated. A more complete answer requires finite sample calculations which is a computationally imposing task. Monte Carlo methods for analysis of the posterior will be explored. ***