A Statistical Analysis of Santa Barbara Ambulance Response in 2006: Performance Under Load

Ambulance response times in Santa Barbara County for 2006 are analyzed using point process techniques, including kernel intensity estimates and K-functions. Clusters of calls result in significantly higher response times, and this effect is quantified. In particular, calls preceded by other calls within 20 km and within the previous hour are significantly more likely to result in violations. This effect appears to be especially pronounced within semi-rural neighborhoods

Clustering in the biotechnology industry

This study uses Poisson regression techniques to analyse the location of biotechnology companies throughout the USA. Three hypotheses are considered: that firms locate in population centres in order to attract workers, that they locate near colleges and universities where potential workers are likely to be better educated, and that they locate in close proximity to research-oriented universities and institutes because high-technology firms frequently spin-off from these research centres. We find that clusters do tend to be located near population centres colleges and universities but the influence of research-based universities is particularly striking. This highlights a powerful policy instrument for regions hoping to promote high-tech industrial clusters: the creation and maintenance of a first-rate research-oriented university. While these ideas have been suggested in the past, our approach to defining, measuring, and analysing these variables provides new insights into their significance, and also suggests avenues for future research

A Note on the Separability of Multidimensional Point Processes with Covariates

For models used to describe multi-dimensional marked point processes with covariates, the high number of parameters typically involved and the high dimensionality of the process can make model evaluation, construction, and estimation using maximum likelihood quite difficult. Conditions are explored here under which parameters governing one set of coordinates or covariates affecting a multi-dimensional marked point process may be estimated separately. The resulting estimates are, under the given conditions, similar to maximum likelihood estimates

Characterization and Simplification of Non-simple Marked Point Processes

Simple point processes are often characterized by their associated compensators or conditional intensities. For non-simple point processes, however, the conditional intensity and compensator do not uniquely determine the distribution of the process. Various ways of characterizing non-simple multivariate point processes are discussed here, some important classes of separable non-simple processes are investigated, and methods of simplification involving thinning, rescaling, and changing the mark space are presented

Consistent Parametric Estimation of the Intensity of a Spatial-temporal Point Process

e consider conditions under which parametric estimates of the intensity of a spatial-temporal point process are consistent. Although the actual point process being estimated may not be Poisson, an estimate involving maximizing a function that corresponds exactly to the log-likelihood if the process is Poisson is consistent under certain simple conditions. A second estimate based on weighted least squares is also shown to be consistent under quite similar assumptions. The conditions for consistency are simple and easily verified, and examples are provided to illustrate the extent to which consistent estimation may be achieved. An important special case is when the point processes being etimated are in fact Poisson, though other important examples are explored as well

Multi-dimensional Residual Analysis of Point Models for Earthquake Occurrences

Methods of examining the fit of multi-dimensional point process models using residual analysis are proposed. One method involves rescaled residuals, obtained by transforming points along one coordinate to form a homogeneous Poisson process inside a random irregular boundary. Both vertical and horizontal forms of this rescaling are discussed. We also present a different method of residual analysis, involving thinning the point process according to the conditional intensity to form a homogeneous Poisson process on the original, untransformed space. These methods for assessing goodness-of-fit are applied to point process models for the space-time-magnitude distribution of earthquake occurrences, using in particular the multi-dimensional versio of Ogata's epidemic-type aftershock sequence (ETAS) model and a 30-year catalog of 580 earthquakes occurring in Bear Valley, California, as an example. The thinned residuals suggest that the fit of the model may be significantly improved by using an anisotropic spatial distance function in the estimation of the spatially varying background rate. Using rescaled residuals, it is shown that the temporal-magnitude distribution of aftershock activity is not separable, and that in particular, in contrast to the ETAS model, the triggering density of earthquakes appears to depend on the magnitude of the secondary events. The residual analysis highlights that the fit of the space-time ETAS model may be substantially improved by allowing the parameters governing the triggering density to vary for earthquakes of different magnitudes. Such modifications are important since the ETAS model is widely used seismology for hazard analysis

A Note on the Separability of Multidimensional Point Processes with Covariates

For models used to describe multi-dimensional marked point processes with covariates, the high number of parameters typically involved and the high dimensionality of the process can make model evaluation, construction, and estimation using maximum likelihood quite difficult. Conditions are explored here under which parameters governing one set of coordinates or covariates affecting a multi-dimensional marked point process may be estimated separately. The resulting estimates are, under the given conditions, similar to maximum likelihood estimates