Minimum Message Length and Statistically Consistent Invariant (Objective?) Bayesian Probabilistic Inference—From (Medical) “Evidence”

References

• Akaike , H. 1970 . Statistical prediction information . Annals of the Institute of Statistical Mathematics , 22 : 203 – 17 .
   Web of Science ®Google Scholar
• Akaike , H. 1973 . “ Information theory and an extension of the maximum likelihood principle ” . In Proceedings of the 2nd international symposium on information theory , Edited by: Petrov , B.N. and Csaki , F. 267 – 81 . Budapest : Akademiai Kiado .
   Google Scholar
• Akaike , H. 1987 . Factor Analysis and AIC . Psychometrika , 52 (3) : 317 – 332 .
   Web of Science ®Google Scholar
• Barron , A. R. and Cover , T. M. 1991 . Minimum complexity density estimation . IEEE Transactions on Information Theory , 37 : 1034 – 54 .
   Web of Science ®Google Scholar
• Berger , J. O. and Wolpert , R. L. 1988 . The likelihood principle , 2nd edition , California, , USA : Hayward . Institute of Mathematical Statistics monograph series
   Google Scholar
• Bernardo , J. M. and Smith , A. F. M. 1994 . Bayesian theory , New York : Wiley .
   Google Scholar
• Chaitin , G. J. 1966 . On the length of programs for computing finite sequences . Journal of the Association for Computing Machinery , 13 : 547 – 69 .
   Web of Science ®Google Scholar
• Clarke , D. M. , Smith , G. C. , Dowe , D. L. and McKenzie , D. P. 2003 . An empirically‐derived taxonomy of common distress syndromes in the medically ill . Journal of Psychosomatic Research , 54 : 323 – 30 .
   PubMed Web of Science ®Google Scholar
• Comley , Joshua W. and Dowe , David L. General Bayesian networks and asymmetric languages . Paper presented at Proceedings of the Hawaii International Conference on Statistics and Related Fields . June 5–8 .
   Google Scholar
• Comley , Joshua W. and Dowe , David L. 2005 . “ Minimum message length and generalized Bayesian nets with asymmetric languages ” . In Chap. 11 in Advances in minimum description length: Theory and applications (MDL handbook) , Edited by: Grünwald , P. , Pitt , M. A. and Myung , I. J. 265 – 94 . Cambridge, MA : MIT Press .
   Google Scholar
• Dowe , D. L. 2007 . Discussion following “Hedging predictions in machine learning, A. Gammerman and V. Vovk” . Computer Journal , 2 (50) : 167 – 8 .
   Google Scholar
• Dowe , D. L. 2008 . Foreword re C. S. Wallace . Computer Journal , 51 (5) : 523 – 560 .
   Web of Science ®Google Scholar
• Dowe , D. L. , Allison , L. , Dix , T. I. , Hunter , L. , Wallace , C. S. and Edgoose , T. 1996 . “ Circular clustering of protein dihedral angles by minimum message length ” . In Pacific symposium on biocomputing ’96 , Edited by: Hunter , L. and Klein , T. 242 – 55 . Singapore : World Scientific .
   Google Scholar
• Dowe , D. L. , Baxter , R. A. , Oliver , J. J. and Wallace , C. S. 1998 . “ Point estimation using the Kullback–Leibler loss function and MML ” . In Proceedings of the 2nd Pacific‐Asia conference on research and development in knowledge discovery and data mining (PAKDD‐98) Volume 1394 of LNAI , Edited by: Wu , X. , Kotagiri , Ramamohanarao and Korb , K. 87 – 95 . Berlin : Springer .
   Google Scholar
• Dowe , D. L. , Farr , G. E. , Hurst , A. J. and Lentin , K. L. Information‐theoretic football tipping . Paper presented at the 3rd Conference on Maths and Computers in Sport . pp. 233 – 41 . [See also Technical Report TR 96/297, Dept. Computer Science, Monash University, Australia 3168, Dec 1996.]
   Google Scholar
• Dowe , D. L. , Gardner , S. and Oppy , G. R. 2007 . Bayes not bust! Why simplicity is no problem for Bayesians . British Journal for the Philosophy of Science , 58 (4) : 709 – 54 .
   Web of Science ®Google Scholar
• Dowe , D. L. and Hajek , A. R. A non‐behavioural, computational extension to the Turing test . Paper presented at the International Conference on Computational Intelligence & Multimedia Applications (ICCIMA’98) . February , Gippsland, Australia. pp. 101 – 6 .
   Google Scholar
• Dowe , D. L. and Korb , K. B. Conceptual difficulties with the efficient market hypothesis: Towards a naturalized economics . Paper presented at the Proceedings on Information, Statistics and Induction in Science (ISIS) . pp. 212 – 23 . [See also Technical Report TR 94/215, Dept. Computer Science, Monash University, Australia 3168, 1994.]
   Google Scholar
• Dowe , D. L. and Krusel , N. 1993 . A decision tree model of bushfire activity Technical report TR 93/190 , Clayton, Vic. 3800, , Australia : Dept. of Computer Science, Monash University . September
   Google Scholar
• Dowe , D. L. , Oliver , J. J. and Wallace , C. S. 1996 . “ MML estimation of the parameters of the spherical Fisher distribution ” . In Algorithmic learning theory, 7th international workshop, ALT ‘96, Sydney, Australia, October 1996, proceedings Volume 1160 of Lecture notes in artificial intelligence , Edited by: Arikawa , S. and Sharma , A. 213 – 227 . Berlin : Springer .
   Google Scholar
• Dowe , D. L. and Oppy , G. R. 2001 . Universal Bayesian inference? . Behavioral and Brain Sciences (BBS) , 24 (4) : 662 – 3 .
   Web of Science ®Google Scholar
• Dowe , D. L. and Wallace , C. S. 1997 . “ Resolving the Neyman–Scott problem by Minimum Message Length ” . In Proceedings of computing science and statistics – 28th symposium on the interface Edited by: Billard , L. and Fisher , N. I. Volume 28 , 614 – 18 . Interface Foundation of North America
   Google Scholar
• Edgoose , T. , Allison , L. and Dowe , D. L. 1998 . “ An MML classification of protein structure that knows about angles and sequence ” . In Pacific symposium on biocomputing ‘98 , Edited by: Altman , R. B. , Dunker , A. K. , Hunter , L. and Klein , T. 585 – 96 . Singapore : World Scientific .
   Google Scholar
• Edwards , R. T. and Dowe , D. L. 1998 . “ Single factor analysis in MML mixture modelling ” . In Proceedings of the 2nd Pacific‐Asia conference on research and development in knowledge discovery and data mining (PAKDD‐98) Volume 1394 of Lecture notes in artificial intelligence (LNAI) , Edited by: Wu , Xindong , Kotagiri , Ramamohanarao and Korb , Kevin B. 96 – 109 . Berlin : Springer .
   Google Scholar
• Fitzgibbon , L. J. , Dowe , D. L. and Vahid , F. Minimum message length autoregressive model order selection . Paper presented at the Proceedings of the International Conference on Intelligent Sensors and Information Processing . January , Chennai, India. pp. 439 – 44 . IEEE (IEEE Press) .
   Google Scholar
• Forster , M. and Sober , E. 1994 . How to tell when simpler, more unified, or less ad hoc theories will provide more accurate predictions . British Journal for the Philosophy of Science , 45 : 1 – 35 .
   Web of Science ®Google Scholar
• Glymour , C. 1981 . “ Why I am not a Bayesian ” . In Theory and Evidence , Edited by: Glymour , C. and Stalker , D. 63 – 93 . Princeton : Princeton University Press .
   Google Scholar
• Grossman , J. Forthcoming . “ The likelihood principle ” . In Handbook for philosophy of science, Volume 7 Philosophy of statistics , New York : Elsevier .
   Google Scholar
• Grünwald , Peter D. and Langford , John . 2007 . Suboptimal behavior of Bayes and MDL in classification under misspecification . Machine Learning , 66 (31) : 119 – 149 .
   Web of Science ®Google Scholar
• Hernández‐Orallo , José . 2000 . Beyond the Turing test . Journal of Logic, Language and Information , 9 (4) : 447 – 66 .
   Google Scholar
• Jeffreys , H. 1946 . An invariant form for the prior probability in estimation problems . Proceedings of the Royal Society of London A , 186 : 453 – 4 .
   Google Scholar
• Kissane , D. W. , Bloch , S. , Dowe , D. L. , Snyder , R. D. , Onghena , P. , McKenzie , D. P. and Wallace , C. S. 1996 . The Melbourne family grief study, I: Perceptions of family functioning in bereavement . American Journal of Psychiatry , 153 : 650 – 8 .
   PubMed Web of Science ®Google Scholar
• Kissane , D. W. , Bloch , S. , Onghena , P. , McKenzie , D. P. , Snyder , R. D. and Dowe , D. L. 1996 . The Melbourne family grief study, II: Psychosocial morbidity and grief in bereaved families . American Journal of Psychiatry , 153 : 659 – 66 .
   PubMed Web of Science ®Google Scholar
• Kolmogorov , A. N. 1965 . Three approaches to the quantitative definition of information . Problems of Information Transmission , 1 : 4 – 7 .
   Google Scholar
• Kornienko , L. , Albrecht , D. W. and Dowe , D. L. 2005a . “ A preliminary MML linear classifier using principal components for multiple classes ” . In Proceedings of the 18th Australian joint conference on artificial intelligence (AI’2005), Volume 3809 of Lecture notes in artificial intelligence (LNAI) Edited by: Zhang , S. and Jarvis , Ray . 922 – 6 . Sydney, , Australia Berlin: Springer
   Google Scholar
• Kornienko , L. , Albrecht , D. W. and Dowe , D. L. 2005b . A preliminary MML linear classifier using principal components for multiple classes Technical report CS 2005/179 , Australia : School of Computer Sci. & Softw. Eng., Monash Univ., Melb. .
   Google Scholar
• Kornienko , Lara , Dowe , David L. and Albrecht , David W. 2002 . “ Message length formulation of support vector machines for binary classification – A preliminary scheme ” . In Proceedings of the 15th Australian Joint Conference on Artificial Intelligence, Volume 2557 of Lecture notes in artificial intelligence (LNAI) , Edited by: McKay , B. and Slaney , J. K. 119 – 130 . Berlin : Springer‐Verlag .
   Google Scholar
• Legg , S. and Hutter , M. 2007 . Universal intelligence: A definition of machine intelligence . Minds and Machines , 17 (4) : 391 – 444 .
   Web of Science ®Google Scholar
• McKenzie , D. P. , McGorry , P. D. , Wallace , C. S. , Low , L. H. , Copolov , D. L. and Singh , B. S. 1993 . Constructing a minimal diagnostic decision tree . Methods in Information in Medicine , 32 : 161 – 6 .
   PubMed Web of Science ®Google Scholar
• Needham , S. L. and Dowe , D. L. Message length as an effective Ockham’s razor in decision tree induction . Paper presented at the 8th International Workshop on Artificial Intelligence and Statistics (AI+STATS 2001) . pp. 253 – 60 .
   Google Scholar
• Neyman , J. and Scott , E. L. 1948 . Consistent estimates based on partially consistent observations . Econometrika , 16 : 1 – 32 .
   Web of Science ®Google Scholar
• Ooi , J. N. and Dowe , D. L. Inferring phylogenetic graphs of natural languages using minimum message length . Paper presented at CAEPIA 2005 (11th Conference of the Spanish Association for Artificial Intelligence) . Volume 1 , pp. 143 – 52 .
   Google Scholar
• Pilowsky , I. , Levine , S. and Boulton , D.M. 1969 . The classification of depression by numerical taxonomy . British Journal of Psychiatry , 115 : 937 – 45 .
   PubMed Web of Science ®Google Scholar
• Prior , M. , Eisenmajer , R. , Leekam , S. , Wing , L. , Gould , J. , Ong , B. and Dowe , D. L. 1998 . Are there subgroups within the autistic spectrum? A cluster analysis of a group of children with autistic spectrum disorders . Journal of Child Psycholology and Psychiatry , 39 (6) : 893 – 902 .
   PubMed Web of Science ®Google Scholar
• Rissanen , J. J. 1978 . Modeling by shortest data description . Automatica , 14 : 465 – 71 .
   Web of Science ®Google Scholar
• Schwarz , G. 1978 . Estimating dimension of a model . Annals of Statistics , 6 : 461 – 4 .
   Web of Science ®Google Scholar
• Shannon , C. E. 1948 . A mathematical theory of communication . The Bell System Technical Journal , 27 : 379 – 423 . 623 – 56 .
   Web of Science ®Google Scholar
• Solomonoff , R. J. 1964 . A formal theory of inductive inference . Information and Control , 7 : 1 – 22 . 224 – 54 .
   Google Scholar
• Tan , P. J. and Dowe , D. L. 2002 . “ MML inference of decision graphs with multi‐way joins ” . In Proceedings of the 15th Australian Joint Conference on Artificial Intelligence, Volume 2557 of Lecture notes in artificial intelligence (LNAI) , Edited by: McKay , R. and Slaney , J. 131 – 42 . Berlin : Springer Verlag .
   Google Scholar
• Tan , P. J. and Dowe , D. L. 2003 . “ MML inference of decision graphs with multi‐way joins and dynamic attributes ” . In Proceedings of the 16th Australian Joint Conference on Artificial Intelligence Volume 2903 of Lecture Notes in Artificial Intelligence (LNAI) , Edited by: Gedeon , T. D. and Chun Che Fung , L. 269 – 81 . Berlin : Springer .
   Google Scholar
• Tan , P. J. and Dowe , D. L. 2004 . “ MML inference of oblique decision trees ” . In Proceedings of the 17th Australian Joint Conference on Artificial Intelligence, Volume 3339 of Lecture Notes in Artificial Intelligence (LNAI) , Edited by: Webb , G. I. and Yu , Xinghuo . 1082 – 8 . Berlin : Springer .
   Google Scholar
• Tan , P. J. and Dowe , D. L. 2006 . “ Decision forests with oblique decision trees ” . In Proceedings of the 5th Mexican international conference on artificial intelligence, Volume 4293 of Lecture Notes in Artificial Intelligence (LNAI) , Edited by: Gelbukh , A. F. and Reyes García , C. A. 593 – 603 . Berlin : Springer .
   Google Scholar
• Tan , P. J. , Dowe , D. L. and Dix , T. I. 2007 . “ Building classification models from microarray data with tree‐based classification algorithms ” . In Proceedings of the 20th Australian Joint Conference on Artificial Intelligence, Volume 4830 of Lecture Notes in Artificial Intelligence (LNAI) , Edited by: Orgun , M. A. and Thornton , J. 589 – 98 . Berlin : Springer .
   Google Scholar
• Vapnik , V. N. 1995 . The nature of statistical learning theory , Berlin : Springer .
   Google Scholar
• Visser , Gerhard and Dowe , D. L. Minimum message length clustering of spatially‐correlated data with varying inter‐class penalties . Proceedings of the 6th IEEE international conference on computer and information science (ICIS) 2007 . pp. 17 – 22 . Piscataway, NJ : IEEE Press .
   Google Scholar
• Wallace , C. S. 1995 . Multiple factor analysis by MML estimation Technical report CS TR 95/218 , Clayton, Victoria 3168, Australia : Dept. of Computer Science, Monash University . Clayton, Melbourne, Australia
   Google Scholar
• Wallace , C. S. 1996 . “ False oracles and SMML estimators ” . In Proceedings of the Information, Statistics and Induction in Science (ISIS) Conference , Edited by: Dowe , D. L. , Korb , K. B. and Oliver , J. J. 304 – 316 . Singapore : World Scientific . [Was previously Tech Rept 89/128, Dept. Comp. Sci., Monash Univ., Australia, June 1989.]
   Google Scholar
• Wallace , C. S. 1997 . On the selection of the order of a polynomial model Technical report, Royal Holloway College, England, UK. Chris released this in 1997 (from Royal Holloway) in the belief that it would become a Royal Holloway Tech Rept dated 1997, but it is not clear that it was ever released there. Soft copy certainly does exist, though. Perhaps see www.csse.monash.edu.au/~dld/CSWallacePublications; INTERNET
   Google Scholar
• Wallace , C. S. 1998 . Intrinsic classification of spatially correlated data . Computer Journal , 41 (8) : 602 – 611 .
   Web of Science ®Google Scholar
• Wallace , C. S. 2005 . Statistical and inductive inference by minimum message length , Berlin : Springer Verlag . Information Science and Statistics series
   Google Scholar
• Wallace , C. S. and Boulton , D. M. 1968 . An information measure for classification . Computer Journal , 11 (2) : 185 – 94 .
   Web of Science ®Google Scholar
• Wallace , C. S. and Boulton , D. M. 1975 . An invariant Bayes method for point estimation . Classification Society Bulletin , 3 (3) : 11 – 34 .
   Google Scholar
• Wallace , C. S. and Dowe , D. L. 1993 . MML estimation of the von Mises concentration parameter Technical Report 93/193 , Clayton 3168, Australia : Dept. of Computer Science, Monash University . December
   Google Scholar
• Wallace , C. S. and Dowe , D. L. Intrinsic classification by MML – the Snob program . Proceedings of the 7th Australian Joint Conference on Artificial Intelligence . Edited by: Zhang , C. , Debenham , J. and Lukose , D. pp. 37 – 44 . Singapore : World Scientific .
   Google Scholar
• Wallace , C. S. and Dowe , D. L. 1999a . Minimum message length and Kolmogorov complexity . Computer Journal , 42 (4) : 270 – 283 .
   Web of Science ®Google Scholar
• Wallace , C. S. and Dowe , D. L. 1999b . Refinements of MDL and MML coding . Computer Journal , 42 (4) : 330 – 337 .
   Web of Science ®Google Scholar
• Wallace , C. S. and Dowe , D. L. 1999c . Rejoinder . Computer Journal , 42 (4) : 345 – 7 .
   Web of Science ®Google Scholar
• Wallace , C. S. and Dowe , D. L. 2000 . MML clustering of multi‐state, Poisson, von Mises circular and Gaussian distributions . Statistics and Computing , 10 (1) : 73 – 83 .
   Web of Science ®Google Scholar
• Wallace , C. S. and Freeman , P. R. 1987 . Estimation and inference by compact coding . Journal of the Royal Statistical Society series B , 49 (3) : 240 – 52 . See also Discussion on pp. 252–65
   Google Scholar
• Wallace , C. S. and Freeman , P. R. 1992 . Single‐factor analysis by minimum message length estimation . Journal of the Royal Statistical Society B , 54 (1) : 195 – 209 .
   Google Scholar