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Robust bayesian estimation

Yuanxi, Yang

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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Robust bayesian estimation

Yuanxi, Yang

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.

Robust bayesian estimation

Yuanxi, Yang

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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Title:

Robust bayesian estimation

Contributors:

Yuanxi, Yang (author)

Published in:

Bulletin géodésique ; 65

Publication date:

1991

ISSN:

DOI:

https://doi.org/10.1007/BF00806343

Type of media:

Article (Journal)

Type of material:

Print

Language:

English

Keywords:

Geodäsie , Geometrie , Geodynamik , Zeitschrift , Mathematik , Mineralogie

Classification:

BKL: 38.30 Mineralogie / 38.73 Geodäsie
Local classification TIB: 275/3200

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