Rohan A. Baxter

Minimum Message Length Segmentation

The segmentation problem arises in many applications in data mining, A.I. and statistics, including segmenting time series, decision tree algorithms and image processing. In this paper, we consider a range of criteria which may be applied to determine if some data should be segmented into two or regions. We develop a information theoretic criterion (MML) for the segmentation of univariate data with Gaussian errors. We perform simulations comparing segmentation methods (MML, AIC, MDL and BIC) and conclude that the MML criterion is the preferred criterion. We then apply the segmentation method to financial time series data.

The Kindest Cut: Minimum Message Length Segmentation

We consider some particular instances of the segmentation problem. We derive minimum message length (MML) expressions for stating the region boundaries for some one and two dimensional examples. It is found the message length cost of stating region boundaries is dependent on the noise of the data in the separated regions and also the ‘degree of separation’ of the two regions.

Bayesian Estimation of the Von Mises Concentration Parameter

The von Mises distribution is a maximum entropy distribution. It corresponds to the distribution of an angle of a compass needle in a uniform magnetic field of direction, μ, with concentration parameter, κ. The concentration parameter, κ, is the ratio of the field strength to the temperature of thermal fluctuations. Previously, we obtained a Bayesian estimator for the von Mises distribution parameters using the information-theoretic Minimum Message Length (MML) principle. Here, we examine a variety of Bayesian estimation techniques by examining the posterior distribution in both polar and Cartesian co-ordinates. We compare the MML estimator with these fellow Bayesian techniques, and a range of Classical estimators. We find that the Bayesian estimators outperform the Classical estimators.

The Loans Standard Model of Credit Money

The Loans Standard (LS) model is an example of a credit monetary system. The LS model encapsulates the credit money characteristics which have been identified in the present monetary system, but abstracts away from other aspects such as commodity and fiat money. In the resulting purely credit monetary model, the implications for interest rates, monetary inflation and the structure of monetary institutions are explored. The LS model can be used to help clarify some of the endogenous credit money issues raised by Moore, Wray, Minsky and others.