Taeryon Choi (Korea University)

Generalized partially additive Bayesian spectral analysis regression models

In this talk, we present a Bayesian method for generalized partially additive regression using a spectral analysis of Gaussian process priors  for the  regression function. The smoothing prior distribution for the spectral coefficients incorporates hyper parameters that control the smoothness of the function and the tradeoff between the data and the prior distribution. We contrast our approach with existing Bayesian regression models for dealing with shape restrictions for the regression function and various noise distributions. The model includes  covariate effects in the generalized partial linear model structure and flexible semiparametric Bayesian model using Dirichlet mixtures. We derive the posterior distributions for these parameters and present numerical schemes to generate posterior samples. We illustrate the empirical performance of the proposed model based on synthetic data and real data applications in comparison with other existing methods. Asymptotic properties of the proposed models are also discussed.