Abstract
Classical least squares Bayesian estimation consists of minimizing the sum of the squared residuals of observations and the corrections to prior estimates of parameters.Many authors have produced more robust versions of this estimation by replacing the square by something else, such as the absolute value. In this article, three robust (M-LS, LS-M and M-M) estimators for three corresponding error models are described based on the principle of maximum likelihood type estimates (M-estimates). The influence functions of the three robust Bayesian estimators are given. The algorithm implementation problems are discussed and the expressions for the posterior variance-covariance are derived.
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Yuanxi, Y. Robust bayesian estimation. Bulletin Géodésique 65, 145–150 (1991). https://doi.org/10.1007/BF00806343
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DOI: https://doi.org/10.1007/BF00806343