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Minimum Message Length and Kolmogorov Complexity
 Computer Journal
, 1999
"... this paper is to describe some of the relationships among the different streams and to try to clarify some of the important differences in their assumptions and development. Other studies mentioning the relationships appear in [1, Section IV, pp. 10381039], [2, sections 5.2, 5.5] and [3, p. 465] ..."
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Cited by 104 (25 self)
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this paper is to describe some of the relationships among the different streams and to try to clarify some of the important differences in their assumptions and development. Other studies mentioning the relationships appear in [1, Section IV, pp. 10381039], [2, sections 5.2, 5.5] and [3, p. 465]
Bayes not Bust! Why Simplicity is no Problem for Bayesians
, 2007
"... The advent of formal definitions of the simplicity of a theory has important implications for model selection. But what is the best way to define simplicity? Forster and Sober ([1994]) advocate the use of Akaike’s Information Criterion (AIC), a nonBayesian formalisation of the notion of simplicity. ..."
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Cited by 13 (10 self)
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The advent of formal definitions of the simplicity of a theory has important implications for model selection. But what is the best way to define simplicity? Forster and Sober ([1994]) advocate the use of Akaike’s Information Criterion (AIC), a nonBayesian formalisation of the notion of simplicity. This forms an important part of their wider attack on Bayesianism in the philosophy of science. We defend a Bayesian alternative: the simplicity of a theory is to be characterised in terms of Wallace’s Minimum Message Length (MML). We show that AIC is inadequate for many statistical problems where MML performs well. Whereas MML is always defined, AIC can be undefined. Whereas MML is not known ever to be statistically inconsistent, AIC can be. Even when defined and consistent, AIC performs worse than MML on small sample sizes. MML is statistically invariant under 1to1 reparametrisation, thus avoiding a common criticism of Bayesian approaches. We also show that MML provides answers to many of Forster’s objections to Bayesianism. Hence an important part of the attack on
MML mixture modelling of multistate, Poisson, von Mises circular and Gaussian distributions
 In Proc. 6th Int. Workshop on Artif. Intelligence and Statistics
, 1997
"... Minimum Message Length (MML) is an invariant Bayesian point estimation technique which is also consistent and efficient. We provide a brief overview of MML inductive inference (Wallace and Boulton (1968), Wallace and Freeman (1987)), and how it has both an informationtheoretic and a Bayesian interp ..."
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Cited by 8 (5 self)
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Minimum Message Length (MML) is an invariant Bayesian point estimation technique which is also consistent and efficient. We provide a brief overview of MML inductive inference (Wallace and Boulton (1968), Wallace and Freeman (1987)), and how it has both an informationtheoretic and a Bayesian interpretation. We then outline how MML is used for statistical parameter estimation, and how the MML mixture modelling program, Snob (Wallace and Boulton (1968), Wallace (1986), Wallace and Dowe(1994)) uses the message lengths from various parameter estimates to enable it to combine parameter estimation with selection of the number of components. The message length is (to within a constant) the logarithm of the posterior probability of the theory. So, the MML theory can also be regarded as the theory with the highest posterior probability. Snob currently assumes that variables are uncorrelated, and permits multivariate data from Gaussian, discrete multistate, Poisson and von Mises circular dist...
Minimum Message Length Clustering of SpatiallyCorrelated Data with Varying InterClass Penalties
 6TH IEEE INTERNATIONAL CONFERENCE ON COMPUTER AND INFORMATION SCIENCE (ICIS 2007
, 2007
"... We present here some applications of the Minimum Message Length (MML) principle to spatially correlated data. Discrete valued Markov Random Fields are used to model spatial correlation. The models for spatial correlation used here are a generalisation of the model used in (Wallace 1998) [14] for uns ..."
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Cited by 5 (3 self)
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We present here some applications of the Minimum Message Length (MML) principle to spatially correlated data. Discrete valued Markov Random Fields are used to model spatial correlation. The models for spatial correlation used here are a generalisation of the model used in (Wallace 1998) [14] for unsupervised classification of spatially correlated data (such as image segmentation). We discuss how our work can be applied to that type of unsupervised classification. We now make the following three new contributions. First, the rectangular grid used in (Wallace 1998) [14] is generalised to an arbitrary graph of arbitrary edge distances. Secondly, we refine (Wallace 1998) [14] slightly by including a discarded message length term important to small data sets and to a simpler problem presented here. Finally, we show how the Minimum Message Length (MML) principle can be used to test for the presence of spatial correlation and how it can be used to choose between models of varying complexity to infer details of the nature of the spatial correlation.
Minimum Message Length Shrinkage Estimation
"... This note considers estimation of the mean of a multivariate Gaussian distribution with known variance within the Minimum Message Length (MML) framework. Interestingly, the resulting MML estimator exactly coincides with the positivepart JamesStein estimator under the choice of an uninformative pri ..."
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This note considers estimation of the mean of a multivariate Gaussian distribution with known variance within the Minimum Message Length (MML) framework. Interestingly, the resulting MML estimator exactly coincides with the positivepart JamesStein estimator under the choice of an uninformative prior. A new approach for estimating parameters and hyperparameters in general hierarchical Bayes models is also presented.
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
Ninimum Message Length and Statistically Consistent Invariant; (Objective?) Bayesian Probabilistic Inference  From (Medical) “Evidence”
 SOCIAL EPISTEMOLOGY VOL. 22, NO. 4, OCTOBER–DECEMBER 2008, PP. 433–460
, 2008
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