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One-sided approximation of Bayes rule and its application to regression model with Cauchy noise. (English) Zbl 0682.62019
The Kullback-Leibler distance (or the relative Shannon entropy) between an unfeasible conditional (on time t) probability density function for a parameter w, p(w\(| t)\), and an admissible approximant \^p(w\(| t)\) is given by \[ I(p,\hat p)=\int \hat p(w| t) \ln (\hat p(w| t)/p(w| t))dw. \] A simple upper bound for this distance is suggested which is based on a one-sided recursively feasible, lower bound on p(w\(| t)\). \^p(w\(| t)\) is then chosen by optimising this bound. This procedure is applied to the problem of Bayesian estimation of the parameters of a linear regression model when the error term has a Cauchy distribution and observations are made over time.
Reviewer: P.W.Jones

MSC:
62F15 Bayesian inference
62J05 Linear regression; mixed models
90C90 Applications of mathematical programming
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