A characterization of conjugate priors in exponential families with application to inverse regression

Wei Luo; Naomi S. Altman

doi:10.1016/j.spl.2012.10.030

A characterization of conjugate priors in exponential families with application to inverse regression

Wei Luo, Naomi S. Altman

Statistics

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1 Scopus citations

Abstract

It is often convenient to assume that X and X {pipe} Y are in the same exponential family. By considering X as the "parameter" and Y as the "data", the problem becomes determining which exponential families X {pipe} Y have conjugate priors. We develop a necessary condition for conjugacy. One-dimensional exponential families can be conjugate only if they have exactly two support points.

Original language	English (US)
Pages (from-to)	650-654
Number of pages	5
Journal	Statistics and Probability Letters
Volume	83
Issue number	2
DOIs	https://doi.org/10.1016/j.spl.2012.10.030
State	Published - Feb 2013

All Science Journal Classification (ASJC) codes

Statistics and Probability
Statistics, Probability and Uncertainty

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10.1016/j.spl.2012.10.030

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abstract = "It is often convenient to assume that X and X {pipe} Y are in the same exponential family. By considering X as the {"}parameter{"} and Y as the {"}data{"}, the problem becomes determining which exponential families X {pipe} Y have conjugate priors. We develop a necessary condition for conjugacy. One-dimensional exponential families can be conjugate only if they have exactly two support points.",

author = "Wei Luo and Altman, {Naomi S.}",

note = "Funding Information: The authors thank the editor and an anonymous reviewer for their proactive comments. The authors acknowledge partial support from NSF DMS 1007801 . Naomi Altman also acknowledges partial support from NSF DMS DMS-1127914 to the Statistical and Applied Mathematical Sciences Institute and from NIH UL1RR033184 .",

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N2 - It is often convenient to assume that X and X {pipe} Y are in the same exponential family. By considering X as the "parameter" and Y as the "data", the problem becomes determining which exponential families X {pipe} Y have conjugate priors. We develop a necessary condition for conjugacy. One-dimensional exponential families can be conjugate only if they have exactly two support points.

AB - It is often convenient to assume that X and X {pipe} Y are in the same exponential family. By considering X as the "parameter" and Y as the "data", the problem becomes determining which exponential families X {pipe} Y have conjugate priors. We develop a necessary condition for conjugacy. One-dimensional exponential families can be conjugate only if they have exactly two support points.

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EP - 654

JO - Statistics and Probability Letters

JF - Statistics and Probability Letters

IS - 2

ER -

A characterization of conjugate priors in exponential families with application to inverse regression

Abstract

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