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Maximum Entropy and Bayesian Methods Fundamental Theories of Physics Maximum Entropy and Bayesian Methods Fundamental Theories of Physics An International Book Series on The Fundamental Theories of Physics: Their Clarification, Development and Application Editor: ALWYN VAN DER MERWE University ofDenver, U.S.A. Editorial Advisory Board: LAWRENCE P. HORWITZ, Tel-Aviv University, Israel BRIAN D. JOSEPHSON, University of Cambridge, U.K. CLIVE KILMISTER, University ofLondon, u.K. PEKKA J. LAHTI, University of Turku, Finland GUNTER LUDWIG, Philipps-Universitiit, Marburg, Germany ASHER PERES, Israel Institute of Technology, Israel NATHAN ROSEN, Israel Institute of Technology, Israel EDUARD PROGOVECKI, University of Toronto, Canada MENDEL SACHS, State University ofNew York at Buffalo, U.S.A. ABDUS SALAM, International Centre for Theoretical Physics, Trieste, Italy HANS-JURGEN TREDER, ZentralinstitutjUr Astrophysik der Akademie der Wissenschaften, Germany Volume 79 Maximum Entropy and Bayesian Methods Santa Fe, New Mexico, U.S.A., 1995 Proceedings of the Fifteenth International Workshop on Maximum Entropy and Bayesian Methods edited by Kenneth M. Hanson Dynamic Experimentation Division, Los Alamos National Laboratory, Los Alamos, New Mexico, U.S.A. and Richard N. Silver Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico, U.S.A. SPRINGER-SCIENCE +BUSINESS MEDIA, B. V. A C.I.P. Catalogue record for this book is available from the Library of Congress ISBN 978-94-010-6284-8 ISBN 978-94-011-5430-7 (eBook) DOI 10.1007/978-94-011-5430-7 Printed on acid-free paper All Rights Reserved © 1996 Springer Science+Business Media Dordrecht Originally published by Kluwer Academic Publishers in 1996 No part of the material protected by this copyright notice may be reproduced or utilized in any form or by any means, electronic or mechanical, inc1uding photocopying, recording or by any information storage and retrieval system, without written permission from the copyright owner. CONTENTS Preface. xiii Participant List. .. xvii WORKSHOP PRESENTATIONS NOT INCLUDED IN THESE PROCEEDINGS. xxi RECONSTRUCTION OF THE PROBABILITY DENSITY FUNCTION IMPLICIT IN OPTION PRICES FROM INCOMPLETE AND NOISY DATA R. J. Hawkins, M. Rubinstein and G. J. Daniell.. .. 1 MODEL SELECTION AND PARAMETER ESTIMATION FOR EXPONENTIAL SIGNALS A. Ramaswami and G. L. Bretthorst. 9 HIERARCHICAL BAYESIAN TIME-SERIES MODELS L. M. Berliner. 15 BAYESIAN TIME SERIES: MODELS AND COMPUTATIONS FOR THE ANALYSIS OF TIME SERIES IN THE PHYSICAL SCIENCES M. West...................................................... 23 MAXENT, MATHEMATICS, AND INFORMATION THEORY I. Csiszar............................................ ; . 35 BAYESIAN ESTIMATION OF THE VON MISES CONCENTRATION PARAMETER D. L. Dowe, 1. J. Oliver, R. A. Baxter and C. S. Wallace. 51 A CHARACTERIZATION OF THE DIRICHLET DISTRIBUTION WITH APPLICATION TO LEARNING BAYESIAN NETWORKS D. Geiger and D. Heckerman. 61 THE BOOTSTRAP IS INCONSISTENT WITH PROBABILITY THEORY D. H. Wolpert. 69 vi CONTENTS DATA-DRIVEN PRIORS FOR HYPERPARAMETERS IN REGULARIZATION D. Keren and M. Wennan. .. 77 MIXTURE MODELING TO INCORPORATE MEANINGFUL CONSTRAINTS INTO LEARNING I. Tchoumatchenko and 1-G. Ganascia. .. .. 85 MAXIMUM ENTROPY (MAXENT) METHOD IN EXPERT SYSTEMS AND INTELLIGENT CONTROL: NEW POSSIBILITIES AND LIMITATIONS V. Kreinovich, H. T. Nguyen and E. A. Walker. 93 THE DE FINETTI TRANSFORM S. 1. Press. 101 CONTINUUM MODELS FOR BAYESIAN IMAGE MATCHING 1. C. Gee and P. D. Peralta. .. 109 MECHANICAL MODELS AS PRIORS IN BAYESIAN TOMOGRAPHIC RECONTRUCTION A. Rangarajan, S.-J. Lee and G. Gindi. .. 117 THE BAYES INFERENCE ENGINE K. M. Hanson and G. S. Cunningham. .. 125 A FULL BAYESIAN APPROACH FOR INVERSE PROBLEM A. Mohammad-Djafari ........................................... 135 PIXON-BASED MULTIRESOLUTION IMAGE RECONSTRUCTION AND QUANTIFICATION OF IMAGE INFORMATION CONTENT R. C. Puetter. .. 145 BAYESIAN MULTIMODAL EVIDENCE COMPUTATION BY ADAPTIVE TEMPERING MCMC M.-D. Wu and W. J. Fitzgerald. .. 153 BAYESIAN INFERENCE AND THE ANALYTIC CONTINUATION OF IMAGINARY-TIME QUANTUM MONTE CARLO DATA J. E. Gubernatis, 1. Bonca and M. Jarrell ............................. 163 CONTENTS vii SPECTRAL PROPERTIES FROM QUANTUM MONTE CARLO DATA: A CONSISTENT APPROACH R. Preuss, W. Von der Linden and W. Hanke. .. .. .. .. .. .. .. .. .. .. .. .. ... 171 AN APPLICATION OF MAXIMUM ENTROPY METHOD TO DYNAMICAL CORRELATION FUNCTIONS AT ZERO TEMPERATURE H. Pang, H. Akhlaghpour and M. Jarrell. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. ... 179 CHEBYSHEV MOMENT PROBLEMS: MAXIMUM ENTROPY AND KERNEL POLYNOMIAL METHODS R. N. Silver, H. Roeder, A. F. Voter and J. D. Kress ....................... , 187 CLUSTER EXPANSIONS AND ITERATIVE SCALING FOR MAXIMUM­ ENTROPY LANGUAGE MODELS J. D. Lafferty and B. Suhm ................................................ 195 A MAXENT TOMOGRAPHY METHOD FOR ESTIMATING FISH DENSITIES IN A COMMERCIAL FISHERY S. Lizamore, M. Vignaux and G. A. Vignaux .............................. 203 TOWARD OPTIMAL OBSERVER PERFORMANCE OF DETECTION AND DISCRIMINATION TASKS ON RECONSTRUCTIONS FROM SPARSE DATA R. F. Wagner, K. J. Myers, D. G. Brown, M. P. Anderson and K. M. Hanson ............................................................. 211 ENTROPIES FOR DISSIPATIVE FLUIDS AND MAGNETOFLUIDS WITHOUT DISCRETIZATION D. Montgomery........................................................... 221 ON THE IMPORTANCE OF Q MARGINALIZATION IN MAXIMUM ENTROPY R. Fischer, W. Von der Linden and V. Dose............................... 229 QUANTUM MECHANICS AS AN EXOTIC PROBABILITY THEORY S. youssef ................................................................. 237 BAYESIAN PARAMETER ESTIMATION OF NUCLEAR-FUSION CONFINEMENT TIME SCALING LAWS V. Dose, W. Von der Linden and A. Garrett.... .. .. .. .. .. .. .. .. .. .. .. ... 245 viii CONTENTS HIERARCHICAL SEGMENTATION OF RANGE AND COLOR IMAGES BASED ON BAYESIAN DECISION THEORY P. Boulanger.............................................................. 251 PRIORS ON MEASURES J. Skilling and S. Sibisi.. .. .. ... .. .. ....... .. .. .. ... .. .. .. ... .. .. .. ... .. 261 DETERMINING WHETHER TWO DATA SETS ARE FROM THE SAME DISTRIBUTION D. H. Wolpert ............................................................. 271 OCCAM'S RAZOR FOR PARAMETRIC FAMILIES AND PRIORS ON THE SPACE OF DISTRIBUTIONS V. Balasubrarnanian ...................................................... 277 SKIN AND MAXIMUM ENTROPY: A HIDDEN COMPLICITY? B. Dubertret, N. Rivier and G. Schliecker .................................. 285 PREDICTING THE ACCURACY OF BAYES CLASSIFIERS R. R. Snapp. .. 295 MAXIMUM ENTROPY ANALYSIS OF GENETIC ALGORITHMS J. L. Shapiro, M. Rattray and A. Priigel-Bennett.......................... 303 DATA FUSION IN THE FIELD OF NON DESTRUCTIVE TESTING S. Gautier, G. Le Besnerais, A. Mohammad-Djafari and B. Lavayssiere............................................................. 311 DUAL STATISTICAL MECHANICAL THEORY FOR UNSUPERVISED AND SUPERVISED LEARNING G. Deco and B. Schiirmann ................................................ 317 COMPLEX SINUSOID ANALYSIS BY BAYESIAN DECONVOLUTION OF THE DISCRETE FOURIER TRANSFORM F. Dublanchet, P. Duvaut and J. Idier. .. 323 STATISTICAL MECHANICS OF CHOICE P. S. Faynzilberg..... .. 329 CONTENTS IX RATIONAL NEURAL MODELS BASED ON INFORMATION THEORY R. L. Fry . 335 A NEW ENTROPY MEASURE WITH THE EXPLICIT NOTION OF COMPLEXITY W. Holender . .. 341 MAXIMUM ENTROPY STATES AND COHERENT STRUCTURES IN MAGNETO HYDRODYNAMICS R. Jordan and B. Thrkington. ... .. .. .. .. ... .. .. ... .. .. ... .. .. .. .. 347 A LOGNORMAL STATE OF KNOWLEDGE P. R. Dukes and E. G. Larson. .. 355 PIXON-BASED MULTIRESOLUTION IMAGE RECONSTRUCTION FOR YOHKOH'S HARD X-RAY TELESCOPE T. Metcl;llf, H. S. Hudson, T. Kosugi, R. C. Puetter and R. K. Pilla.. .. 361 BAYESIAN METHODS FOR INTERPRETING PLUTONIUM URINALYSIS DATA G. Miller and W. C. Inkret. .. 367 THE INFORMATION CONTENT OF SONAR ECHOES R. Pitre.. .. 375 OBJECTIVE PRIOR FOR COSMOLOGICAL PARAMETERS G. Evrard ................................................................. 381 MEAL ESTIMATION: ACCEPTABLE-LIKELIHOOD EXTENSIONS OF MAXENT P. S. Faynzilberg..... .. 387 ON CURVE FITTING WITH TWO-DIMENSIONAL UNCERTAINTIES F. H. Frohner. .. 393 BAYESIAN INFERENCE IN SEARCH FOR THE IN VIVO T2 DECAY-RATE DISTRIBUTION IN HUMAN BRAIN I. Gideoni. .. 407 x CONTENTS BAYESIAN COMPARISON OF FIT PARAMETERS: APPLICATION TO TIME-RESOLVED X-RAY SPECTROSCOPY V. Kashyap . .. 413 EDGE ENTROPY AND VISUAL COMPLEXITY P. Moos and J. P. Lewis ................................................... 419 MAXIMUM ENTROPY TOMOGRAPHY C. T. Mottershead . .. ... .. .. .. .. .. .. .. .. ... .. .. .. .... .. .. .. ... .. .. .. ... 425 BAYESIAN REGULARIZATION OF SOME SEISMIC OPERATORS M. D. Sacchi and T. J. Ulrych ............................................. 431 MULTIMODALITY BAYESIAN ALGORITHM FOR IMAGE RECONSTRUCTION IN POSITRON EMISSION TOMOGRAPHY S. Sastry, 1. W Vanmeter and R.E. Carson . .. 437 EVIDENCE INTEGRALS W. Von der Linden, R. Fischer and V. Dose............................... 443 Index ..................................................................... 449 The Workshop coordinator, Barbara Rhodes, in between the cochairs, Ken Hanson (left) and Richard Silver at the Bradbury Science Museum in Los Alamos. Wlodek Holender gets greeted by Barbara Rhodes and Rose Vigil. PREFACE The Fifteenth International Workshop on Maximum Entropy and Bayesian Meth­ ods was held July 31-August 4, 1995 in Santa Fe, New Mexico, USA. St. John's College, located in the foothills of the Sangre de Cristo Mountains,
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