Jump to ContentJump to Main Navigation
Pattern TheoryFrom representation to inference$
Users without a subscription are not able to see the full content.

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

Show Summary Details
Page of

PRINTED FROM OXFORD SCHOLARSHIP ONLINE (oxford.universitypressscholarship.com). (c) Copyright Oxford University Press, 2022. All Rights Reserved. An individual user may print out a PDF of a single chapter of a monograph in OSO for personal use.date: 03 July 2022

Jump Diffusion Inference In Complex Scenes

Jump Diffusion Inference In Complex Scenes

Chapter:
(p.532) 19 Jump Diffusion Inference In Complex Scenes
Source:
Pattern Theory
Author(s):

Ulf Grenander

Michael I. Miller

Publisher:
Oxford University Press
DOI:10.1093/oso/9780198505709.003.0020

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

Oxford Scholarship Online requires a subscription or purchase to access the full text of books within the service. Public users can however freely search the site and view the abstracts and keywords for each book and chapter.

Please, subscribe or login to access full text content.

If you think you should have access to this title, please contact your librarian.

To troubleshoot, please check our FAQs , and if you can't find the answer there, please contact us .