Related papers: Space and circular time log Gaussian Cox processes…
A Gaussian Cox process is a popular model for point process data, in which the intensity function is a transformation of a Gaussian process. Posterior inference of this intensity function involves an intractable integral (i.e., the…
Point pattern data often exhibit features such as abrupt changes, hotspots and spatially varying dependence in local intensity. Under a Poisson process framework, these correspond to discontinuities and nonstationarity in the underlying…
Rich new marked point process data allow researchers to consider disparate problems such as the factors affecting the location and type of police use of force incidents, and the characteristics that impact the location and size of forest…
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…
The log-Gaussian Cox process is a flexible and popular class of point pattern models for capturing spatial and space-time dependence for point patterns. Model fitting requires approximation of stochastic integrals which is implemented…
The paper considers a Cox process where the stochastic intensity function for the Poisson data model is itself a non-homogeneous Poisson process. We show that it is possible to obtain the marginal data process, namely a non-homogeneous…
Circular data arise in many areas of application. Recently, there has been interest in looking at circular data collected separately over time and over space. Here, we extend some of this work to the spatio-temporal setting, introducing…
In this paper we present a novel inference methodology to perform Bayesian inference for spatiotemporal Cox processes where the intensity function depends on a multivariate Gaussian process. Dynamic Gaussian processes are introduced to…
Point processes in time have a wide range of applications that include the claims arrival process in insurance or the analysis of queues in operations research. Due to advances in technology, such samples of point processes are increasingly…
To obtain operational insights regarding the crime of burglary in London we consider the estimation of effects of covariates on the intensity of spatial point patterns. By taking into account localised properties of criminal behaviour, we…
Doubly-stochastic point processes model the occurrence of events over a spatial domain as an inhomogeneous Poisson process conditioned on the realization of a random intensity function. They are flexible tools for capturing spatial…
Crime has both varying patterns in space, related to features of the environment, economy, and policing, and patterns in time arising from criminal behavior, such as retaliation. Serious crimes may also be presaged by minor crimes of…
Hawkes processes are point process models that have been used to capture self-excitatory behavior in social interactions, neural activity, earthquakes and viral epidemics. They can model the occurrence of the times and locations of events.…
While the presence of clustering in crime and security event data is well established, the mechanism(s) by which clustering arises is not fully understood. Both contagion models and history independent correlation models are applied, but…
Spatio-temporal processes in environmental applications are often assumed to follow a Gaussian model, possibly after some transformation. However, heterogeneity in space and time might have a pattern that will not be accommodated by…
From a statistical point of view, crime data present certain peculiarities that have led to a growing interest in their analysis. In particular, a characteristic that some property crimes frequently present is the existence of uncertainty…
We study the problem of non-parametric Bayesian estimation of the intensity function of a Poisson point process. The observations are $n$ independent realisations of a Poisson point process on the interval $[0,T]$. We propose two related…
Analyzing crime events is crucial to understand crime dynamics and it is largely helpful for constructing prevention policies. Point processes specified on linear networks can provide a more accurate description of crime incidents by…
This paper proposes a new methodology to perform Bayesian inference for a class of multidimensional Cox processes in which the intensity function is piecewise constant. Poisson processes with piecewise constant intensity functions are…
Statistical modeling of point patterns is an important and common problem in several areas. The Poisson process is the most common process used for this purpose, in particular, its generalization that considers the intensity function to be…