Maximum posterior estimate and its statistic properties

Abstract

Based on an extended Gauss-Markov model where the unknown parameters has the prior normal distribution, this paper derives the maximum posterior estimate formulas of the parameters which are proved to be unbiased, efficient, and of variance of unit weight which is biased. Finally, the marginal maximum posterior estimate formula of the variance with unbiased and efficient properties is derived.

Keywords

parameters / variance / statistical distribution / marginal distributions / maximum-posterior estimation