On Bayesian estimation of densities and sampling distributions: The posterior predictive distribution as the Bayes estimator

Agustín G. Nogales

Statistica Neerlandica, 2022, vol. 76, issue 2, 236-250

Abstract: Optimality results for three interesting Bayesian estimation problems are presented in this paper: the estimation of the sampling distribution for the squared total variation function, the estimation of the density for the L1‐squared loss function and the estimation of a real distribution function for the L∞‐squared loss function. The posterior predictive distribution provides the solution to these problems. Some examples are presented to illustrate it.

Date: 2022
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