Log-normal linear regression models are popular in many fields of research.Bayesian estimation of the conditional mean of the dependent variable is problematic as many choices of the prior for the variance (on the log-scale) lead to posterior distributions with no finite moments. We propose a generalized inverse Gaussian prior for this variance and derive the conditions on the prior parameters that yield posterior distributions of the conditional mean of thedependent variable with finite moments up to a pre-specified order. The conditions depend on one of the three parameters of the suggested prior; the other two have an influence on inferences for small and medium sample sizes. A second goal of this paper is to discuss how to choose these parameters according to different criteria including the optimization of frequentist properties of posterior means.

Bayesian Conditional Mean Estimation in Log-Normal Linear Regression Models with Finite Quadratic Expected Loss

TRIVISANO, CARLO
2016

Abstract

Log-normal linear regression models are popular in many fields of research.Bayesian estimation of the conditional mean of the dependent variable is problematic as many choices of the prior for the variance (on the log-scale) lead to posterior distributions with no finite moments. We propose a generalized inverse Gaussian prior for this variance and derive the conditions on the prior parameters that yield posterior distributions of the conditional mean of thedependent variable with finite moments up to a pre-specified order. The conditions depend on one of the three parameters of the suggested prior; the other two have an influence on inferences for small and medium sample sizes. A second goal of this paper is to discuss how to choose these parameters according to different criteria including the optimization of frequentist properties of posterior means.
2016
Enrico, Fabrizi; Carlo, Trivisano
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11585/568956
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