bsamGP: An R Package for Bayesian Spectral Analysis Models Using Gaussian Process Priors

Abstract

The Bayesian spectral analysis model (BSAM) is a powerful tool to deal with semiparametric methods in regression and density estimation based on the spectral representation of Gaussian process priors. The bsamGP package for R provides a comprehensive set of programs for the implementation of fully Bayesian semiparametric methods based on BSAM. Currently, bsamGP includes semiparametric additive models for regression, generalized models and density estimation. In particular, bsamGP deals with constrained regression models with monotone, convex/concave, S-shaped and U-shaped functions by modeling derivatives of regression functions as squared Gaussian processes. bsamGP also contains Bayesian model selection procedures for testing the adequacy of a parametric model relative to a non-specific semiparametric alternative and the existence of the shape restriction. To maximize computational efficiency, we carry out posterior sampling algorithms of all models using compiled Fortran code. The package is illustrated through Bayesian semiparametric analyses of synthetic data and benchmark data.

Keywords

• cosine basis
• gaussian process priors
• markov chain monte carlo
• r
• shape restrictions
• semiparametric models
• spectral representation