The Prior-Predictive Value: A Paradigm of Nasty Multi-Dimensional Integrals

W. Von Der Linden, R. Preuss, V. Dose

Research output: Chapter in Book/Report/Conference proceedingConference contributionResearch

Abstract

At the heart of Bayesian model comparison lies the so-called prior-predictive value. In the important class of Quantified-MaxEnt applications analytic approximations are routinely used which often give rise to noise-fitting and ringing. We present an improved analytic expression which overcomes these shortcomings. In most interesting real-world problems, however, standard approximations and straight forward application of Markov-Chain Monte Carlo are hampered by the complicated structure of the likelihood in parameter space. At the Maxent workshop 1997 in Boise John Skilling suggested to employ a formalism, borrowed from Statistical physics, to compute the prior-predictive value. We have scrutinized his suggestion: IT WORKS!
Original languageEnglish
Title of host publicationMaximum Entropy and Bayesian Methods Garching, Germany 1998
EditorsWolfgang von der Linden, Volker Dose, Rainer Fischer, Roland Preuss
PublisherSpringer Netherlands
Pages319-326
Number of pages8
ISBN (Print)978-94-010-5982-4 978-94-011-4710-1
Publication statusPublished - 1999

Publication series

NameFundamental Theories of Physics
PublisherSpringer Netherlands

Fingerprint

Markov chains
approximation
suggestion
formalism
physics

Keywords

  • Artificial Intelligence (incl. Robotics), Bayes factor, Coding and Information Theory, Discrete Mathematics in Computer Science, MCMC, model comparison, Prior-predictive value, Probability Theory and Stochastic Processes, Statistics, general

Cite this

Linden, W. V. D., Preuss, R., & Dose, V. (1999). The Prior-Predictive Value: A Paradigm of Nasty Multi-Dimensional Integrals. In W. V. D. Linden, V. Dose, R. Fischer, & R. Preuss (Eds.), Maximum Entropy and Bayesian Methods Garching, Germany 1998 (pp. 319-326). (Fundamental Theories of Physics). Springer Netherlands.

The Prior-Predictive Value: A Paradigm of Nasty Multi-Dimensional Integrals. / Linden, W. Von Der; Preuss, R.; Dose, V.

Maximum Entropy and Bayesian Methods Garching, Germany 1998. ed. / Wolfgang von der Linden; Volker Dose; Rainer Fischer; Roland Preuss. Springer Netherlands, 1999. p. 319-326 (Fundamental Theories of Physics).

Research output: Chapter in Book/Report/Conference proceedingConference contributionResearch

Linden, WVD, Preuss, R & Dose, V 1999, The Prior-Predictive Value: A Paradigm of Nasty Multi-Dimensional Integrals. in WVD Linden, V Dose, R Fischer & R Preuss (eds), Maximum Entropy and Bayesian Methods Garching, Germany 1998. Fundamental Theories of Physics, Springer Netherlands, pp. 319-326.
Linden WVD, Preuss R, Dose V. The Prior-Predictive Value: A Paradigm of Nasty Multi-Dimensional Integrals. In Linden WVD, Dose V, Fischer R, Preuss R, editors, Maximum Entropy and Bayesian Methods Garching, Germany 1998. Springer Netherlands. 1999. p. 319-326. (Fundamental Theories of Physics).
Linden, W. Von Der ; Preuss, R. ; Dose, V. / The Prior-Predictive Value: A Paradigm of Nasty Multi-Dimensional Integrals. Maximum Entropy and Bayesian Methods Garching, Germany 1998. editor / Wolfgang von der Linden ; Volker Dose ; Rainer Fischer ; Roland Preuss. Springer Netherlands, 1999. pp. 319-326 (Fundamental Theories of Physics).
@inproceedings{20a1618a297849a4b4525235fd3a9a24,
title = "The Prior-Predictive Value: A Paradigm of Nasty Multi-Dimensional Integrals",
abstract = "At the heart of Bayesian model comparison lies the so-called prior-predictive value. In the important class of Quantified-MaxEnt applications analytic approximations are routinely used which often give rise to noise-fitting and ringing. We present an improved analytic expression which overcomes these shortcomings. In most interesting real-world problems, however, standard approximations and straight forward application of Markov-Chain Monte Carlo are hampered by the complicated structure of the likelihood in parameter space. At the Maxent workshop 1997 in Boise John Skilling suggested to employ a formalism, borrowed from Statistical physics, to compute the prior-predictive value. We have scrutinized his suggestion: IT WORKS!",
keywords = "Artificial Intelligence (incl. Robotics), Bayes factor, Coding and Information Theory, Discrete Mathematics in Computer Science, MCMC, model comparison, Prior-predictive value, Probability Theory and Stochastic Processes, Statistics, general",
author = "Linden, {W. Von Der} and R. Preuss and V. Dose",
note = "DOI: 10.1007/978-94-011-4710-131",
year = "1999",
language = "English",
isbn = "978-94-010-5982-4 978-94-011-4710-1",
series = "Fundamental Theories of Physics",
publisher = "Springer Netherlands",
pages = "319--326",
editor = "Linden, {Wolfgang von der} and Volker Dose and Rainer Fischer and Roland Preuss",
booktitle = "Maximum Entropy and Bayesian Methods Garching, Germany 1998",
address = "Netherlands",

}

TY - GEN

T1 - The Prior-Predictive Value: A Paradigm of Nasty Multi-Dimensional Integrals

AU - Linden, W. Von Der

AU - Preuss, R.

AU - Dose, V.

N1 - DOI: 10.1007/978-94-011-4710-131

PY - 1999

Y1 - 1999

N2 - At the heart of Bayesian model comparison lies the so-called prior-predictive value. In the important class of Quantified-MaxEnt applications analytic approximations are routinely used which often give rise to noise-fitting and ringing. We present an improved analytic expression which overcomes these shortcomings. In most interesting real-world problems, however, standard approximations and straight forward application of Markov-Chain Monte Carlo are hampered by the complicated structure of the likelihood in parameter space. At the Maxent workshop 1997 in Boise John Skilling suggested to employ a formalism, borrowed from Statistical physics, to compute the prior-predictive value. We have scrutinized his suggestion: IT WORKS!

AB - At the heart of Bayesian model comparison lies the so-called prior-predictive value. In the important class of Quantified-MaxEnt applications analytic approximations are routinely used which often give rise to noise-fitting and ringing. We present an improved analytic expression which overcomes these shortcomings. In most interesting real-world problems, however, standard approximations and straight forward application of Markov-Chain Monte Carlo are hampered by the complicated structure of the likelihood in parameter space. At the Maxent workshop 1997 in Boise John Skilling suggested to employ a formalism, borrowed from Statistical physics, to compute the prior-predictive value. We have scrutinized his suggestion: IT WORKS!

KW - Artificial Intelligence (incl. Robotics), Bayes factor, Coding and Information Theory, Discrete Mathematics in Computer Science, MCMC, model comparison, Prior-predictive value, Probability Theory and Stochastic Processes, Statistics, general

M3 - Conference contribution

SN - 978-94-010-5982-4 978-94-011-4710-1

T3 - Fundamental Theories of Physics

SP - 319

EP - 326

BT - Maximum Entropy and Bayesian Methods Garching, Germany 1998

A2 - Linden, Wolfgang von der

A2 - Dose, Volker

A2 - Fischer, Rainer

A2 - Preuss, Roland

PB - Springer Netherlands

ER -