### Abstract

Original language | English |
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Title of host publication | Maximum Entropy and Bayesian Methods Garching, Germany 1998 |

Editors | Wolfgang von der Linden, Volker Dose, Rainer Fischer, Roland Preuss |

Publisher | Springer Netherlands |

Pages | 319-326 |

Number of pages | 8 |

ISBN (Print) | 978-94-010-5982-4 978-94-011-4710-1 |

Publication status | Published - 1999 |

### Publication series

Name | Fundamental Theories of Physics |
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Publisher | Springer Netherlands |

### Fingerprint

### 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

*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.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › Research

*Maximum Entropy and Bayesian Methods Garching, Germany 1998.*Fundamental Theories of Physics, Springer Netherlands, pp. 319-326.

}

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 -