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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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##### References:
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