Wallace, C.S. and Freeman, P.R. (1992). Single factor analysis by MML estimation, J Royal Stat. Soc. B. 54, 1, 195-209, 1992.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....also be used to test implementations of MML estimators in computer programs. If I wish to compare one MML estimator to another, I can evaluate I estimator1 I estimator2 . in the MML derivation have been breached. Other MML like estimators have been developed to allow for altered assumptions [155]. MML and Bayesianism This chapter was written with the objective of providing an introduction for statisticians to MML inference, via Bayesian methods . I examine the relationship between Bayesianism and Minimum Message Length (MML) inference. The main message of this chapter is that MML is ....

....Secondly, we may find that the mean of the posterior is in a region with little probability associated with it, as shown in Figure 3.4 . This second criticism may appear artificial. However, there are models where symmetric multimodal posteriors exist. For example, in Factor Analysis [155], a sign ambiguity means that posteriors will always be symmetric about 0. Bayesian Factor Analysis has therefore tended to use the mode as an estimate [2, 116] Median. Selecting the median of the posterior has the property that it IS invariant under non linear transformations. However, ....

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C.S. Wallace and P.R. Freeman. Single Factor Analysis by MML estimation. J. R. Statist. Soc. B., 54(1):185--209, 1992.

....must first consider the question of how relevance should be measured. Our current research on this problem aims at finding an information theoretic definition of relevance. Our approach is based on the Minimum Message Length inference method developed by Prof. Chris Wallace at Monash University [174, 13, 175, 173, 176, 126]. Appendix A The k means Algorithm The k means algorithm is a well known clustering technique in pattern recognition because of its usually good behaviour and simplicity. It is an iterative scheme which starts from an initial distribution of cluster centres in data space. At each iteration, a ....

C.S. Wallace and P.R. Freeman. Single factor analysis by MML estimation. Journal of the Royal Statistical Society (Series B), 54(1):185--209, 1992.

....be fractional see Oliver and Hand [OH94, Section 2.8] for details. In this paper we consider message length estimates for sufficiently regular models 1 and identically and independently distributed data. Message length estimates can, of course, be made for other cases, see Wallace and Freeman [WF92] for an example. 2 Differences The MML and MDL principles for inductive inference are similar, but distinct. We state these principles, but first define the terms: model and model class. In any inductive inference problem, a set of models is entertained. This model set is often considered to be ....

C.S. Wallace and P.R. Freeman. Single factor analysis by MML estimation. J. R. Statist. Soc. B., 54(1):185--209, 1992.

....Secondly, we may find that the mean of the posterior is in a region with little probability associated with it, as shown in Figure 4 4 . This second criticism may appear artificial. However, there are models where symmetric multimodal posteriors exist. For example, in Factor Analysis [32], a sign ambiguity means that posteriors will always be symmetric about 0. Bayesian Factor Analysis has therefore tended to use the mode as an estimate [1, 21] ffl Median. Selecting the median of the posterior has the property that it IS invariant under nonlinear transformations. However, it ....

....variance) frame, det(F ( v) N 2 2 v 3 . Let us assume a prior distribution over values of oe: h(oe) oe 2 (1 oe 2 ) 3 2 12 The requirement that the determinant of a Fisher Information matrix be non zero is used here, but is not strictly necessary (for example Wallace and Freeman [32] or Wallace and Dowe [30, Page 8] Then the equivalent prior in the (mean, variance) frame is h(v) h(oe) J where J = v oe = 2oe, and hence: h(v) 1 4 (1 v) 3 2 We find the ratio of prior to square root of the Fisher Information remains the same in each parameterisation: h(oe) p ....

C.S. Wallace and P.R. Freeman. Single factor analysis by MML estimation. Journal of the Royal Statistical Society (Series B), 54:195--209, 1992.

....similar to the set of useful models constructed in MML.We have reservations about MDL s emphasis on model classes rather than fully specified models. It loses the ability of MML to make parameter estimates often superior to the maximum likelihood estimates typically used in conjunction with MDL [17, 18, 19, 20]. Also, in some problems, e.g. mixture modelling, two competing hypotheses of the same formal structure but differing parameter values may really represent models with markedly different conceptual structure, and lumping these together in the same class seems little different from conflating ....

.... grows in proportion to the data, e.g. mixture modelling, factor analysis and the Neyman Scott problem, MML is known in theory and can be seen in practice to give consistent results, where maximum likelihood, Akaike s information criterion (AIC) and related classical techniques are known to fail [17, 18, 20, 31]. We have found MML to give statistical estimators with good performance on some difficult distributions [19] and to handle easily complex model selection problems such as the inference of causal nets [35] Mindful of the Bayesianism inherent in streams one and two (see Sections 5 and 7) this ....

Wallace, C. S. and Freeman, P. R. (1992) Single factor analysis by MML estimation. J. R. Statist. Soc.,B,54, 195-- 209.

....to the set of useful models constructed in MML. We have reservations about MDL s emphasis on model classes rather than fully specified models. It loses the ability of MML to make parameter estimates often superior to the Maximum Likelihood estimates typically used in conjunction with MDL [17, 18, 19, 20]. Also, in some problems e.g. mixture modelling, two competing hypotheses of the same formal structure but differing parameter values may really represent models with markedly different conceptual structure, and lumping these together in the same class seems little different from conflating ....

.... grows in proportion to the data, e.g. mixture modelling, factor analysis and the Neyman Scott problem, MML is known in theory and can be seen in practice to give consistent results, where Maximum Likelihood, Akaike s Information Criterion (AIC) and related classical techniques are known to fail [31, 17, 18, 20]. We have found MML to give statistical estimators with good performance on some difficult distributions [19] and to handle easily complex model selection problems such as the inference of causal nets [35] Mindful of the Bayesianism inherent in streams one and two (see Sections 5 7) this ....

C. S. Wallace and P. R. Freeman, Single factor analysis by MML estimation, J. Royal Statist. Soc. B 54 (1) (1992) 195--209.

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C.S. Wallace and P.R. Freeman, Single Factor Analysis by MML Estimation, J.R. Statist. Soc. B,54(1), 195-209, 1992.

....modelling conditions. As well as having been applied to mixture models (discussed here) MML has also been successfully applied to a variety of problems of parameter estimation[37, 38, 43, 36, 39, 40, 14, 16] hypothesis testing[43, 39] Hidden Markov Models[19] and other multi variate models[43, 36, 44, 35, 16]. Further references are given in [13] 8 Notes on further work and Snob program extensions The Snob program currently implicitly assumes that variables are independent and uncorrelated. This could be modified to permit single linear (Gaussian) factor analysis[44] or multiple linear (Gaussian) ....

....models[43, 36, 44, 35, 16] Further references are given in [13] 8 Notes on further work and Snob program extensions The Snob program currently implicitly assumes that variables are independent and uncorrelated. This could be modified to permit single linear (Gaussian) factor analysis[44] or multiple linear (Gaussian) factor analysis[35] or to model correlations via an inverse Wishart or some other such prior. It would not be too difficult[41] to permit the user to modify the colourless priors (see Section 2) used by Snob to better represent the user s prior beliefs (or ....

C.S. Wallace and P.R. Freeman. Single factor analysis by MML estimation. Journal of the Royal Statistical Society (Series B), 54:195--209, 1992.

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Wallace, C.S. and Freeman, P.R. (1992). Single factor analysis by MML estimation, J Royal Stat. Soc. B. 54, 1, 195-209, 1992.

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C.S. Wallace and P.R. Freeman. Single factor analysis by MML estimation. Journal of the Royal Statistical Society (Series B), 54:195--209, 1992.

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