J.B. Duke Professor of Statistics and Decision Sciences
We view the locations and times of a collection of crime events as a space-time point pattern. So, with either a nonhomogeneous Poisson process or with a more general Cox
process, we need to specify a space-time intensity. For the latter, we need a random intensity which we model as a realization of a spatio-temporal log Gaussian process. In fact, we view time as circular, necessitating valid separable and nonseparable covariance functions over a
bounded spatial region crossed with circular time. In addition, crimes are classified by crime type. Furthermore, each crime event is marked by day of the year which we convert to day of the week.
We present models to accommodate such data. Then, we extend the modeling to include the marks. Our specifications naturally take the form of hierarchical models which we fit within a Bayesian framework. In this regard, we consider model comparison between the nonhomogeneous Poisson process and the log Gaussian Cox process. We also compare
separable vs. nonseparable covariance specifications.
Our motivating dataset is a collection of crime events for the city of San Francisco during the year 2012. Again, we have location, hour, day of the year, and crime type for each event. We investigate a rich range of models to enhance our understanding of the set of incidences.
Alan E. Gelfand is The James B Duke Professor of Statistical Science at Duke University. He is former chair of the Department of Statistical Science (DSS) and enjoys a secondary appointment as Professor of Environmental Science and Policy in the Nicholas School. Author of more than 260 papers (more than 200 since 1990), Gelfand is internationally known for his contributions to applied statistics, Bayesian computation and Bayesian inference. (An article in Science Watch found him to be the tenth most cited mathematical scientist in the world over the period 1991-2001). Gelfand is an Elected Fellow of the American Statistical Association, the Institute of Mathematical Statistics, and the International Society for Bayesian Analysis. He is an Elected Member of the International Statistical Institute. He is a former President of the International Society for Bayesian Analysis and in 2006 he received the Parzen Prize for a lifetime of research contribution to Statistics. In 2012, he was chosen to give the distinguished Mahalanobis lectures. In 2013, he received a Distinguished Achievement Medal from the ASA Section on Statistics in the Environment.