When Do Ordered Prior Distributions Induce Ordered Posterior Distributions?

18 Pages Posted: 23 Feb 2007  

Ben Klemens

U.S. Department of the Treasury, Office of Tax Analysis (OTA)

Date Written: February 22, 2007

Abstract

It has been shown that if two probability distributions satisfy the monotone likelihood ratio property (MLRP), and are independently updated using common public information and traditional Bayesian updating, then the resulting two posterior distributions will also satisfy the MLRP. I discuss this result and extend it by characterizing the full set of updating operations which preserve the MLRP in this manner, of which Bayesian updating is an element. I also find the set of updating operations which preserve first order stochastic dominance (FOSD). The only operator which preserves both the MLRP and FOSD is that which ignores all new information.

Keywords: monotone ordering, FOSD, MLRP, bayesian updating

JEL Classification: D81, D83

Suggested Citation

Klemens, Ben, When Do Ordered Prior Distributions Induce Ordered Posterior Distributions? (February 22, 2007). Available at SSRN: https://ssrn.com/abstract=964720 or http://dx.doi.org/10.2139/ssrn.964720

Ben Klemens (Contact Author)

U.S. Department of the Treasury, Office of Tax Analysis (OTA) ( email )

1500 Pennsylvania Ave., N.W.
Washington, DC 22203
United States

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