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Advances in Info-MetricsInformation and Information Processing across Disciplines$
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Min Chen, J. Michael Dunn, Amos Golan, and Aman Ullah

Print publication date: 2020

Print ISBN-13: 9780190636685

Published to Oxford Scholarship Online: December 2020

DOI: 10.1093/oso/9780190636685.001.0001

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PRINTED FROM OXFORD SCHOLARSHIP ONLINE (oxford.universitypressscholarship.com). (c) Copyright Oxford University Press, 2021. All Rights Reserved. An individual user may print out a PDF of a single chapter of a monograph in OSO for personal use. date: 17 June 2021

Rényi Divergence and Monte Carlo Integration

Rényi Divergence and Monte Carlo Integration

(p.400) 15 Rényi Divergence and Monte Carlo Integration
Advances in Info-Metrics

John Geweke

Garland Durham

Oxford University Press

Rényi divergence is a natural way to measure the rate of information flow in contexts like Bayesian updating. This chapter shows how Monte Carlo integration can be used to measure Rényi divergence when (as is often the case) only kernels of the relevant probability densities are available. The chapter further demonstrates that Rényi divergence is central to the convergence and efficiency of Monte Carlo integration procedures in which information flow is controlled. It uses this perspective to develop more flexible approaches to the controlled introduction of information; in the limited set of examples considered here, these alternatives enhance efficiency.

Keywords:   Rényi divergence, importance sampling, acceptance sampling, Monte Carlo integration, power concentration, sequential Monte Carlo, adaptive Bayesian learning, optimization

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