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Pattern TheoryFrom representation to inference$
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Ulf Grenander and Michael I. Miller

Print publication date: 2006

Print ISBN-13: 9780198505709

Published to Oxford Scholarship Online: November 2020

DOI: 10.1093/oso/9780198505709.001.0001

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Jump Diffusion Inference In Complex Scenes

Jump Diffusion Inference In Complex Scenes

(p.532) 19 Jump Diffusion Inference In Complex Scenes
Pattern Theory

Ulf Grenander

Michael I. Miller

Oxford University Press

This chapter explores random sampling algorithms introduced in for generating conditional expectations in hypothesis spaces in which there is a mixture of discrete, disconnected subsets. Random samples are generated via the direct simulation of a Markov process whose state moves through the hypothesis space with the ergodic property that the transition distribution of the Markov process converges to the posterior distribution. This allows for the empirical generation of conditional expectations under the posterior. To accommodate the connected and disconnected nature of the state spaces, the Markov process is forced to satisfy jump–diffusion dynamics. Through the connected parts of the parameter space (Lie manifolds) the algorithm searches continuously, with sample paths corresponding to solutions of standard diffusion equations. Across the disconnected parts of parameter space the jump process determines the dynamics. The infinitesimal properties of these jump–diffusion processes are selected so that various sample statistics converge to their expectation under the posterior.

Keywords:   Echiverria theorem, acceptance probability, drift vectors, flight path generation, jump transition measures, pose estimation, total jump intensity

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