Spatio-Temporal Low Count Processes with Application to Violent Crime Events

There is significant interest in being able to predict where crimes will happen, for example to aid in the efficient tasking of police and other protective measures. We aim to model both the temporal and spatial dependencies often exhibited by violent crimes in order to make such predictions. The temporal variation of crimes typically follows patterns familiar in time series analysis, but the spatial patterns are irregular and do not vary smoothly across the area. Instead we find that spatially disjoint regions exhibit correlated crime patterns. It is this indeterminate inter-region correlation structure along with the low-count, discrete nature of counts of serious crimes that motivates our proposed forecasting tool. In particular, we propose to model the crime counts in each region using an integer-valued first order autoregressive process. We take a Bayesian nonparametric approach to flexibly discover a clustering of these region-specific time series. We then describe how to account for covariates within this framework. Both approaches adjust for seasonality. We demonstrate our approach through an analysis of weekly reported violent crimes in Washington, D.C. between 2001-2008. Our forecasts outperform standard methods while additionally providing useful tools such as prediction intervals

A rigorous statistical framework for spatio-temporal pollution prediction and estimation of its long-term impact on health

In the United Kingdom, air pollution is linked to around 40000 premature deaths each year, but estimating its health effects is challenging in a spatio-temporal study. The challenges include spatial misalignment between the pollution and disease data; uncertainty in the estimated pollution surface; and complex residual spatio-temporal autocorrelation in the disease data. This article develops a two-stage model that addresses these issues. The first stage is a spatio-temporal fusion model linking modeled and measured pollution data, while the second stage links these predictions to the disease data. The methodology is motivated by a new five-year study investigating the effects of multiple pollutants on respiratory hospitalizations in England between 2007 and 2011, using pollution and disease data relating to local and unitary authorities on a monthly time scale

A Bayesian localised conditional auto-regressive model for estimating the health effects of air pollution

Estimation of the long-term health effects of air pollution is a challenging task, especially when modeling spatial small-area disease incidence data in an ecological study design. The challenge comes from the unobserved underlying spatial autocorrelation structure in these data, which is accounted for using random effects modeled by a globally smooth conditional autoregressive model. These smooth random effects confound the effects of air pollution, which are also globally smooth. To avoid this collinearity a Bayesian localized conditional autoregressive model is developed for the random effects. This localized model is flexible spatially, in the sense that it is not only able to model areas of spatial smoothness, but also it is able to capture step changes in the random effects surface. This methodological development allows us to improve the estimation performance of the covariate effects, compared to using traditional conditional auto-regressive models. These results are established using a simulation study, and are then illustrated with our motivating study on air pollution and respiratory ill health in Greater Glasgow, Scotland in 2011. The model shows substantial health effects of particulate matter air pollution and nitrogen dioxide, whose effects have been consistently attenuated by the currently available globally smooth models

Package ecespa

Documentation for the R-package "ecespa

The intensity JND comes from Poisson neural noise: Implications for image coding

While the problems of image coding and audio coding have frequently been assumed to have similarities, specific sets of relationships have remained vague. One area where there should be a meaningful comparison is with central masking noise estimates, which define the codec's quantizer step size. In the past few years, progress has been made on this problem in the auditory domain (Allen and Neely, J. Acoust. Soc. Am., {\bf 102}, 1997, 3628-46; Allen, 1999, Wiley Encyclopedia of Electrical and Electronics Engineering, Vol. 17, p. 422-437, Ed. Webster, J.G., John Wiley \& Sons, Inc, NY). It is possible that some useful insights might now be obtained by comparing the auditory and visual cases. In the auditory case it has been shown, directly from psychophysical data, that below about 5 sones (a measure of loudness, a unit of psychological intensity), the loudness JND is proportional to the square root of the loudness \DL(\L) \propto \sqrt{\L(I)}. This is true for both wideband noise and tones, having a frequency of 250 Hz or greater. Allen and Neely interpret this to mean that the internal noise is Poisson, as would be expected from neural point process noise. It follows directly that the Ekman fraction (the relative loudness JND), decreases as one over the square root of the loudness, namely \DL/\L \propto 1/\sqrt{\L}. Above {\L} = 5 sones, the relative loudness JND \DL/\L \approx 0.03 (i.e., Ekman law). It would be very interesting to know if this same relationship holds for the visual case between brightness \B(I) and the brightness JND \DB(I). This might be tested by measuring both the brightness JND and the brightness as a function of intensity, and transforming the intensity JND into a brightness JND, namely \DB(I) = \B(I+ \DI) - \B(I) \approx \DI \frac{d\B}{dI}. If the Poisson nature of the loudness relation (below 5 sones) is a general result of central neural noise, as is anticipated, then one would expect that it would also hold in vision, namely that \DB(\B) \propto \sqrt{\B(I)}. %The history of this problem is fascinating, starting with Weber and Fechner. It is well documented that the exponent in the S.S. Stevens' power law is the same for loudness and brightness (Stevens, 1961) \nocite{Stevens61a} (i.e., both brightness \B(I) and loudness \L(I) are proportional to $I^{0.3}$). Furthermore, the brightness JND data are more like Riesz's near miss data than recent 2AFC studies of JND measures \cite{Hecht34,Gescheider97}