Conditionally reducible natural exponential families and enriched conjugate priors
type: Item
instance of: scholarly article
zbMATH Open document ID: 0973.62011
DOI: 10.1111/1467-9469.00243
author: Guido Consonni
author: Piero Veronese
published in: Scandinavian Journal of Statistics
publication date: 2001-09-16T00:00:00Z
Mathematics Subject Classification ID: 62E10
Mathematics Subject Classification ID: 62F15
zbMATH DE Number: 1646338
zbMATH Keywords: conditional reducibility
zbMATH Keywords: exponential families
zbMATH Keywords: simple quadratic variance families
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1111/1467-9469.00243
OpenAlex ID: W2053822759
title: Conditionally reducible natural exponential families and enriched conjugate priors
review text: The authors consider multidimensional natural exponential families (NEF) of distributions and introduce the notion of conditionally reducible NEF (cr-NEF), i.e., a NEF whose density can be represented as a product of NEFs' densities at lower dimensions (components). (Note that these densities are conditional for fixed ``previous'' observations, so they can be functions of these observations).NEWLINENEWLINENEWLINEA structure of cr-NEF is described and conditions of conditional reducibility are given. For cr-NEFs the notion of enriched standard conjugate (ESCF) family is introduced. ESCF is not a standard conjugate prior for the NEF, but rather a product of independent standard conjugate priors of its components. So such families are richer than the standard conjugate priors. As an application, NEFs with simple quadratic variance functions are considered.
description: scientific article; zbMATH DE number 1646338