Alternatives to Lavine's algorithm for calculation of posterior bounds given convex sets of distributions - Robotics Institute Carnegie Mellon University

Alternatives to Lavine’s algorithm for calculation of posterior bounds given convex sets of distributions

Fabio Cozman
Tech. Report, CMU-RI-TR-97-38, Robotics Institute, Carnegie Mellon University, December, 1997
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Abstract

This paper presents alternatives to Lavine's algorithm, currently the most popular method for calculation of expectation bounds induced by sets of probability distributions. The White-Snow algorithm is first analyzed and demonstrated to be superior to Lavine's algorithm in a variety of situations. The calculation of posterior bounds is then reduced to a fractional programming problem. From the unifying perspective of fractional programming, Lavine's algorithm is identical to Dinkelbach's algorithm, and the White-Snow algorithm is essentially identical to the Charnes-Cooper transformation. A novel algorithm for expectation bounds is given for the situation where both prior and likelihood functions are specified as convex sets of distributions.

BibTeX

@techreport{Cozman-1997-14547,
author = {Fabio Cozman},
title = {Alternatives to Lavine's algorithm for calculation of posterior bounds given convex sets of distributions},
year = {1997},
month = {December},
institute = {Carnegie Mellon University},
address = {Pittsburgh, PA},
number = {CMU-RI-TR-97-38},
}
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