Title: 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.