Latent variable models represent the probability density of data in a space of several dimensions in terms of a smaller number of latent, or hidden, variables. A familiar example is factor analysis which is based on a linear transformations between the latent space and the data space. In this paper we introduce a form of non-linear latent variable model called the Generative Topographic Mapping for which the parameters of the model can be determined using the EM algorithm. GTM provides a principled alternative to the widely used Self-Organizing Map (SOM) of Kohonen (1982), and overcomes most of the significant limitations of the SOM. We demonstrate the performance of the GTM algorithm on a toy problem and on simulated data from flow diagnostics for a multi-phase oil pipeline. Copyright c○MIT Press (1998). 1

We survey the literature on methods for inference and learning in Bayesian Networks composed of discrete and continuous nodes, in which the continuous nodes have a multivariate Gaussian distribution, whose mean and variance depends on the values of the discrete nodes. We also briefly consider hybrid Dynamic Bayesian Networks, an extension of switching Kalman filters. This report is meant to summarize what is known at a sufficient level of detail to enable someone to implement the algorithms, but without dwelling on formalities.

Abstract. A single band texture-based burn scar identi � cation algorithm incorporating the use of grey level co-occurrence matrices with a low pass � ltering technique is described and demonstrated using 1km resolution ATSR-2 imagery of burned savannas in southern Sudan. The algorithm results are compared to those produced by the iterative intensity-based isodata classi � cation technique. The accuracy of each of these methods was evaluated by comparison with 18 m spatial resolution imagery. For a set of 22 sample � re scars of varying area Pearson correlation coeYcients of 0.75 and 0.94 were obtained between the burnt area statistics produced with the low-spatial resolution texture and isodata methods respectively and those produced using the high-resolution data. The classi � cation quality, as described by the Kappa (k) statistic, produced values of k =0.558 and k =0.852. Texture is shown to be an image variable TEXTURE ISODATA capable of highlighting burned area in low spatial resolution imagery, but the currently tested approach oVers no accuracy of quality bene � t over the solely intensity-based method. 1.

We discuss issues arising when a spatial pattern is observed within some bounded region of space, and one wishes to predict the process outside of this region (extrapolation) as well as to perform inference on features of the pattern that cannot be observed (interpolation). We focus on spatial cluster analysis. Here the interpolation arises from the fact that the centres of clustering are not observed. We take a Bayesian approach with a repulsive Markov prior, derive the posterior distribution of the complete data, i.e. cluster centres with associated offspring marks, and propose an adaptive coupling from the past algorithm to sample from this posterior. The approach is illustrated by means of the redwood data set (Ripley, 1977).

In this paper weinvestigate the mathematical modelling of imperfect maintenance of a system under competing risk. The model we propose is strongly motivated byBrown & Proschan's imperfect repair model, but extended to model preventive maintenance as one of several competing risks. Parameter estimation in the model is based on Markov Chain Monte Carlo simulation. The method is tested using a real-life dataset from the OREDA database, and the results are compared to those of other standard repair models.

Searching for failures in the Peruvian labor market via mixture models ¤ Draft-Please do not site