Asymptotic properties and approximation of Bayesian logspline density estimators for communication-free parallel computing methods

Abstract

In this article we perform an asymptotic analysis of Bayesian parallel density estimators which are based on logspline density estimation. The parallel estimator we introduce is in the spirit of a kernel density estimator introduced in recent studies. We provide a numerical procedure that produces the density estimator itself in place of the sampling algorithm. We then derive an error bound for the mean integrated squared error for the full data posterior density estimator. We also investigate the parameters that arise from logspline density estimation and the numerical approximation procedure. Our investigation identifies specific choices of parameters for logspline density estimation that result in the error bound scaling appropriately in relation to these choices.Comment: 33 pages, 11 figure