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

10/25/2017

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by   Alexey Miroshnikov, et al.

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In this article we perform an asymptotic analysis of Bayesian parallel density estimators which are based on logspline density estimation presented in Stone and Koo (1986). The parallel estimator we introduce is in the spirit of the kernel density estimator presented by Neiswanger, Wang and Xing (2015). We provide a numerical procedure that produces the density estimator itself in place of the sampling algorithm. We derive an error bound for the mean integrated squared error for the full data posterior estimator and investigate the parameters that arise from the logspline density estimation and the numerical approximation procedure. Our investigation leads to the choice of parameters that result in the error bound scaling appropriately in relation to them.