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This article concerns the statistical modelling of emergency service response times. We apply advanced methods from spatial survival analysis to deliver inference for data collected by the London Fire Brigade on response times to reported dwelling fires. Existing approaches to the analysis of these data have been mainly descriptive; we describe and demonstrate the advantages of a more sophisticated approach. Our final parametric proportional hazards model includes harmonic regression terms to describe how response time varies with time-of-day and shared spatially correlated frailties on an auxiliary grid for computational efficiency. We investigate the short-term impact of fire station closures in 2014. Whilst the London Fire Brigade are working hard to keep response times down, our findings suggest there is a limit to what can be achieved logistically: the present article identifies areas around the now closed Belsize, Downham, Kingsland, Knightsbridge, Silvertown, Southwark, Wesminster and Woolwich fire stations in which there should perhaps be some concern as to the provision of fire services.

This article was motivated by the desire to improve Markov chain Monte Carlo methods for spatial survival models in which the locations of individuals in space are known. For a dataset comprising information on n individuals, standard methods of MCMC-based inference involve computing the inverse of an n by n matrix at each iteration. However with a judicious choice of auxiliary variables on a regular grid with m prediction points it will be shown how to fit an essentially equivalent model but with a substantially reduced computational cost. For a fixed output grid, the computational cost of the new method is reduced from O(n^3) to O(n); the cost of increasing the output grid size being O(m\log m). Furthermore, the new method simultaneously solves the problem of spatial prediction of functions of the latent field, which for standard methods usually presents a further computational challenge. We apply the new method to a spatial survival dataset previously analysed in Henderson et. al 2002 and show how the new method can be applied to spatial and spatiotemporal geostatistical datasets with the same computational benefits.

In this paper we first describe the class of log-Gaussian Cox processes (LGCPs) as models for spatial and spatio-temporal point process data. We discuss inference, with a particular focus on the computational challenges of likelihood-based inference. We then demonstrate the usefulness of the LGCP by describing four applications: estimating the intensity surface of a spatial point process; investigating spatial segregation in a multi-type process; constructing spatially continuous maps of disease risk from spatially discrete data; and real-time health surveillance. We argue that problems of this kind fit naturally into the realm of geostatistics, which traditionally is defined as the study of spatially continuous processes using spatially discrete observations at a finite number of locations. We suggest that a more useful definition of geostatistics is by the class of scientific problems that it addresses, rather than by particular models or data formats., Comment: Published in at http://dx.doi.org/10.1214/13-STS441 the Statistical Science (http://www.imstat.org/sts/) by the Institute of Mathematical Statistics (http://www.imstat.org)

We investigate two options for performing Bayesian inference on spatial log-Gaussian Cox processes assuming a spatially continuous latent field: Markov chain Monte Carlo (MCMC) and the integrated nested Laplace approximation (INLA). We first describe the device of approximating a spatially continuous Gaussian field by a Gaussian Markov random field on a discrete lattice, and present a simulation study showing that, with careful choice of parameter values, small neighbourhood sizes can give excellent approximations. We then introduce the spatial log-Gaussian Cox process and describe MCMC and INLA methods for spatial prediction within this model class. We report the results of a simulation study in which we compare MALA and the technique of approximating the continuous latent field by a discrete one, followed by approximate Bayesian inference via INLA over a selection of 18 simulated scenarios. The results question the notion that the latter technique is both significantly faster and more robust than MCMC in this setting; 100,000 iterations of the MALA algorithm running in 20 minutes on a desktop PC delivered greater predictive accuracy than the default \verb=INLA= strategy, which ran in 4 minutes and gave comparative performance to the full Laplace approximation which ran in 39 minutes., Comment: This replaces the previous version of the report. The new version includes results from an additional simulation study, and corrects an error in the implementation of the INLA-based methods

This paper introduces an R package for spatio-temporal prediction and forecasting for log-Gaussian Cox processes. The main computational tool for these models is Markov chain Monte Carlo and the new package, lgcp, therefore also provides an extensible suite of functions for implementing MCMC algorithms for processes of this type. The modelling framework and details of inferential procedures are first presented before a tour of lgcp functionality is given via a walk-through data-analysis. Topics covered include reading in and converting data, estimation of the key components and parameters of the model, specifying output and simulation quantities, computation of Monte Carlo expectations, post-processing and simulation of data sets.

This paper reviews results from two projects designed to yield photometry on uniform zero points for five clusters--Coma, the Hyades, M67, NGC 752, and Praesepe. Contributing papers for a project on Cousins VRI photometry and a project on Stromgren-beta photometry are listed. Results of zero point tests of the photometry are reviewed, and their character is found to be satisfactory at the level of a few mmag. Responses to extant criticisms of the photometry are offered, and a section on B-V photometry for the five clusters is included. Because the results of the projects suggest that certain changes should be made in current perspectives on photometry, those changes are reviewed. Finally, suggestions are made about future uses of data from the projects.

This paper introduces a new model and methodology for estimating the ability of NBA players. The main idea is to directly measure how good a player is by comparing how their team performs when they are on the court as opposed to when they are off it. This is achieved in a such a way as to control for the changing abilities of the other players on court at different times during a match. The new method uses multiple seasons' data in a structured way to estimate player ability in an isolated season, measuring separately defensive and offensive merit as well as combining these to give an overall rating. The use of game statistics in predicting player ability will be considered. Results using data from the 2008/9 season suggest that LeBron James, who won the NBA MVP award, was the best overall player. The best defensive player was Lamar Odom and the best rookie was Russell Westbrook, neither of whom won an NBA award that season. The results further indicate that whilst the frequently-reported game statistics provide some information on offensive ability, they do not perform well in the prediction of defensive ability., Comment: 16 pages, 2 figures

Sequential Monte Carlo (SMC) methods are not only a popular tool in the analysis of state space models, but offer an alternative to MCMC in situations where Bayesian inference must proceed via simulation. This paper introduces a new SMC method that uses adaptive MCMC kernels for particle dynamics. The proposed algorithm features an online stochastic optimization procedure to select the best MCMC kernel and simultaneously learn optimal tuning parameters. Theoretical results are presented that justify the approach and give guidance on how it should be implemented. Empirical results, based on analysing data from mixture models, show that the new adaptive SMC algorithm (ASMC) can both choose the best MCMC kernel, and learn an appropriate scaling for it. ASMC with a choice between kernels outperformed the adaptive MCMC algorithm of Haario et al. (1998) in 5 out of the 6 cases considered., Comment: 41 pages, 1 figure