No. 1100

Title:

A Bayesian analysis of Tweedie generalized linear models using a conjugate prior

Author(s):

Ohnishi, Toshio (The Institute of Statistical Mathematics);
Dunn, Peter (University of the Sunshine Coast)

Key words:

common slope, conjugate analysis, empirical Bayesian estimation, location-dispersion family, logarithmic-link, optimal estimating function, power variance, Pythagorean relationship, Tweedie distribution

Abstract:

    We investigate a logarithmic-link generalized linear model, whose underlying sampling density is in an exponential family distribution with power variance function. The distribution coincides with a Possion sum of gamma distributions, known as Tweedie distribution. The multiple-strata case is studied with a common slope and stratum-dependent intercepts. We prove that there exists a conjugate prior density on the intercept parameter, and the conjugate analysis is discussed. An estimation procedure is given, which includes the optimal estimating function of the parameters other than the intercept, and an empirical Baysian estimation of the hyper-parameters of the prior density. As an example, rainfall data for Queensland, Australia, is analyzed.