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Bayesian Posterior Comprehension via Message from Monte Carlo
, 2003
"... We discuss the problem of producing an epitome, or brief summary, of a Bayesian posterior distribution  and then investigate a general solution based on the Minimum Message Length (MML) principle. Clearly, the optimal criterion for choosing such an epitome is determined by the epitome's intended us ..."
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We discuss the problem of producing an epitome, or brief summary, of a Bayesian posterior distribution  and then investigate a general solution based on the Minimum Message Length (MML) principle. Clearly, the optimal criterion for choosing such an epitome is determined by the epitome's intended use. The interesting general case is where this use is unknown since, in order to be practical, the choice of epitome criterion becomes subjective. We identify a number of desirable properties that an epitome could have  facilitation of point estimation, human comprehension, and fast approximation of posterior expectations. We call these the properties of Bayesian Posterior Comprehension and show that the Minimum Message Length principle can be viewed as an epitome criterion that produces epitomes having these properties. We then present and extend Message from Monte Carlo as a means for constructing instantaneous Minimum Message Length codebooks (and epitomes) using Markov Chain Monte Carlo methods. The Message from Monte Carlo methodology is illustrated for binary regression, generalised linear model, and multiple changepoint problems.
A Preliminary MML Linear Classifier using Principal Components for Multiple Classes
"... In this paper we improve on the supervised classification method developed in Kornienko et al. (2002) by the introduction of Principal Components Analysis to the inference process. We also extend the classifier from dealing with binomial (twoclass) problems only to multinomial (multiclass) problem ..."
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In this paper we improve on the supervised classification method developed in Kornienko et al. (2002) by the introduction of Principal Components Analysis to the inference process. We also extend the classifier from dealing with binomial (twoclass) problems only to multinomial (multiclass) problems. The application to which the MML criterion has been applied in this paper is the classification of objects via a linear hyperplane, where the objects are able to come from any multiclass distribution. The inclusion of Principal Component Analysis to the original inference scheme reduces the bias present in the classifierâ€™s search technique. Such improvements lead to a method which, when compared against three commercial Support Vector Machine (SVM) classifiers on Binary data, was found to be as good as the most successful SVM tested. Furthermore, the new scheme is able to classify objects of a multiclass distribution with just one hyperplane, whereas SVMs require several hyperplanes.
Colour Terms, Syntax and Bayes Modelling Acquisition and Evolution
, 2004
"... This thesis investigates language acquisition and evolution, using the methodologies of Bayesian inference and expressioninduction modelling, making specific reference to colour term typology, and syntactic acquisition. In order to test Berlin and Kay's (1969) hypothesis that the typological pat ..."
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This thesis investigates language acquisition and evolution, using the methodologies of Bayesian inference and expressioninduction modelling, making specific reference to colour term typology, and syntactic acquisition. In order to test Berlin and Kay's (1969) hypothesis that the typological patterns observed in basic colour term systems are produced by a process of cultural evolution under the influence of universal aspects of human neurophysiology, an expressioninduction model was created. Ten artificial people were simulated, each of which was a computational agent. These people could learn colour term denotations by generalizing from examples using Bayesian inference, and the resulting denotations had the prototype properties characteristic of basic colour terms.
Minimum Message Length Inference Using Markov Chain Monte Carlo Methods
, 2004
"... xxi Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . xxvii 1 ..."
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xxi Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . xxvii 1
MMLD Inference of the Poisson and Geometric Models
"... Abstract. This paper examines MMLDbased approximations for the inference of two univariate probability densities: the geometric distribution, parameterised in terms of a mean parameter, and the Poisson distribution. The focus is on both parameter estimation and hypothesis testing properties of the ..."
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Abstract. This paper examines MMLDbased approximations for the inference of two univariate probability densities: the geometric distribution, parameterised in terms of a mean parameter, and the Poisson distribution. The focus is on both parameter estimation and hypothesis testing properties of the approximation. The new parameter estimators are compared to the MML87 estimators in terms of bias, squared error risk and KL divergence risk. Empirical experiments demonstrate that the MMLD parameter estimates are more biased, and feature higher squared error risk than the corresponding MML87 estimators. In contrast, the two criteria are virtually indistinguishable in the hypothesis testing experiment. 1
Advance Access publication on June 18, 2008 doi:10.1093/comjnl/bxm117
"... One of the second generation of computer scientists, Chris Wallace completed his tertiary education in 1959 with a Ph.D. in nuclear physics, on cosmic ray showers, under Dr Paul George at Sydney University. Needless to say, computer science was not, at that stage, an established academic discipline. ..."
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One of the second generation of computer scientists, Chris Wallace completed his tertiary education in 1959 with a Ph.D. in nuclear physics, on cosmic ray showers, under Dr Paul George at Sydney University. Needless to say, computer science was not, at that stage, an established academic discipline. With Max Brennan 1 andJohnMaloshehaddesignedand built a large automatic data logging system for recording cosmic ray air shower events and with Max Brennan also developed a complex computer programme for Bayesian analysis of cosmic ray events on the recently installed SILLIAC computer. Appointed lecturer in Physics at Sydney in 1960 he was sent almost immediately to the University of Illinois to copy the design of ILLIAC II, a duplicate of which was to be built at Sydney. ILLIAC II was not in fact completed at that stage and, after an initial less than warm welcome by a department who seemed unsure exactly what this Australian was doing in their midst, his talents were recognized and he was invited to join their staff (under very generous conditions) to assist in ILLIAC II design 2. He remained there for two years helping in particular to design the input output channels and aspects of the advanced control unit (first stage pipeline). In the event, Sydney decided it would be too expensive to build a copy of ILLIAC II, although a successful copy (the Golem) was built in Israel using circuit designs developed by Wallace and Ken Smith. In spite of the considerable financial and academic inducements to remain in America, Wallace returned to Australia after three months spent in England familiarizing himself with the KDF9 computer being purchased by Sydney University to replace SILLIAC. Returning to the School of Physics he joined the Basser