A Journey through Bayesian Nonparametrics: Modeling Regression Functions and Densities with Gaussian Processes
This talk summaries some work on nonparametric Bayesian estimation that uses spectral representations for Gaussian processes. The method results in flexible functions that avoid the straight jacket of parametric models. The model uses hierarchical Bayes priors that control the amount of smoothness of the functions and the tradeoff between the data and the prior distribution. One advantage of the Bayesian approach is that one does not need to conduct cross validation to estimate these smoothing parameters and uses Bayes theorem to estimate them. The models are also extended to include shape constraints. For instance, increasing (decreasing) functions, convex (concave) function, U-shaped and S-shaped functions. The shape constraints can significantly increase estimation accuracy. Various examples will be discussed.
More information on Prof. Dr. Peter Lenk can be found at: https://michiganross.umich.edu/faculty-research/faculty/peter-lenk