We present a simple and powerful method for extrapolating nite-volume Monte Carlo data to in nite volume, based on nite-size-scaling theory. We discuss carefully its systematic and statistical errors, and we illustrate it using three examples: the two-dimensional three-state Potts antiferromagnet on the square lattice, and the two-dimensional O(3) and O(1) -models. In favorable cases it is possible to obtain reliable extrapolations (errors of a few percent) even when the correlation length is 1000 times larger than the lattice.

Disease cluster detection and evaluation have commonly used spatial statistics methods that scan the map with a fixed circular window to locate candidate clusters. Recently, there has been interest in searching for clusters with arbitrary shape. The circular scan test retains high power of detecting a cluster, but does not necessarily identify the exact regions contained in a non-circular cluster particularly well. We propose, implement and evaluate a new procedure that is fast and produces clusters estimates of arbitrary shape in a rich class of possible cluster candidates. We showed that our methods contain the so-called upper level set method as a particular case. We present a power study of our method and, among other results, the main conclusion is that the likelihood-based arbitrarily shaped scan method is not appropriate to find a cluster estimate. When the parameter space includes the set of all possible spatial clusters in a map, a large and discrete parameter space, maximum likely cluster estimates tend to overestimate the true cluster by a large extent. This calls for a new approach different from the maximum likelihood method for this important public health problem.

A novel deformable template is presented which detects and localizes shapes in grayscale images. The template is formulated as a Bayesian graphical model of a two-dimensional shape contour, and it is matched to the image using a variant of the belief propagation (BP) algorithm used for inference on graphical models. The algorithm can localize a target shape contour in a cluttered image and can accommodate arbitrary global translation and rotation of the target as well as significant shape deformations, without requiring the template to be initialized in any special way (e.g. near the target).The use of BP removes a serious restriction imposed in related earlier work, in which the matching is performed by dynamic programming and thus requires the graphical model to be tree-shaped (i.e. without loops). Although BP is not guaranteed to converge when applied to inference on non-tree-shaped graphs, we find empirically that it does converge even for deformable template models with one or more loops. To speed up the BP algorithm, we augment it by a pruning procedure and a novel technique, inspired by the 20 Questions (divide-and-conquer) search strategy, called "focused message updating." These modifications boost the speed of convergence by over an order of magnitude, resulting in an algorithm that detects and localizes shapes in grayscale images in as little as several seconds on an 850 MHz AMD processor.

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We study the antiferromagnetic q-state Potts model on the square lattice for q = 3 and q = 4, using the Wang-Swendsen-Koteck y Monte Carlo algorithm and a new nite-size-scaling extrapolation method. For q = 3 we obtain good control up to correlation length 5000; the data are consistent with ( ) =