The concept of a miss-distance, or error, between a reference quantity and its estimated/controlled value, plays a fundamental role in any filtering/control problem. Yet there is no satisfactory notion of a miss-distance in the well-established field of multi-object filtering. In this paper, we outline the inconsistencies of existing metrics in the context of multi-object miss-distances for performance evaluation. We then propose a new mathematically and intuitively consistent metric that addresses the drawbacks of current multi-object performance evaluation metrics.

We study the approximation of arbitrary distributions P on d-dimensional space by distributions with log-concave density. Approximation means minimizing a Kullback-Leibler-type functional. We show that such an approximation exists if and only if P has finite first moments and is not supported by some hyperplane. Furthermore we show that this approximation depends continuously on P with respect to Mallows distance D1(·, ·). This result implies consistency of the maximum likelihood estimator of a log-concave density under fairly general conditions. It also allows us to prove existence and consistency of estimators in regression models with a response Y = µ(X) + ε, where X and ε are independent, µ(·) belongs to a certain class of regression functions while ε is a random error with logconcave density and mean zero.

In Geographical Information Systems, spatial point pattern data are often analysed by dividing space into pixels, recording the presence or absence of points in each pixel, and fitting a logistic regression. We study weaknesses of this approach, propose improvements, and demonstrate an application to prospective geology in Western Australia. Models based on different pixel grids are incompatible (a 'change-of-support' problem) unless the pixels are very small. On a fine pixel grid, a spatial logistic 1151 A. Baddeley et al./Spatial logistic regression regression is approximately a Poisson point process with loglinear intensity; we give explicit distributional bounds. For a loglinear Poisson process, the optimal parameter estimator from pixel data is not spatial logistic regression, but complementary log-log regression with an offset depending on pixel area. If the pixel raster is randomly subsampled, logistic regression is conditionally optimal. Bias and efficiency depend strongly on the spatial regularity of the covariates. For discontinuous covariates, we propose a new algorithmic strategy in which pixels are subdivided, and demonstrate its efficiency.

Finding solutions to the classical transportation problem is of great importance, since this optimization problem arises in many engineering and computer science applications. Especially the Earth Mover's Distance is used in a plethora of applications ranging from content-based image retrieval, shape matching, fingerprint recognition, object tracking and phishing web page detection to computing color differences in linguistics and biology. Our starting point is the well-known revised simplex algorithm, which iteratively improves a feasible solution to optimality. The Shortlist Method that we propose substantially reduces the number of candidates inspected for improving the solution, while at the same time balancing the number of pivots required. Tests on simulated benchmarks demonstrate a considerable reduction in computation time for the new method as compared to the usual revised simplex algorithm implemented with state-of-the-art initialization and pivot strategies. As a consequence, the Shortlist Method facilitates the computation of large scale transportation problems in viable time. In addition we describe a novel method for finding an initial feasible solution which we coin Modified Russell's Method.

Most metrics between finite point measures currently used in the literature have the flaw that they do not treat differing total masses in an adequate manner for applications. This paper introduces a new metricd 1 that combines positional differences of points under a closest match with the relative difference in total mass in a way that fixes this flaw. A comprehensive collection of theoretical results aboutd 1 and its induced Wasserstein metric d 2 for point process distributions are given, including examples of usefuld 1 -Lipschitz continuous functions,d 2 upper bounds for Poisson process approximation, andd 2 upper and lower bounds between distributions of point processes of i.i.d. points. Furthermore, we present a statistical test for multiple point pattern data that demonstrates the potential ofd 1 in applications.