On spatial and spatio-temporal multi-structure point process models

Spatial and spatio-temporal single-structure point process models are widely used in epidemiology, biology, ecology, seismology... . However, most natural phenomena present multiple interaction structure or exhibit dependence at multiple scales in space and/or time, leading to define new spatial and spatio-temporal multi-structure point process models. In this paper, we investigate and review such multi-structure point process models mainly based on Gibbs and Cox processes

A spatial capture-recapture model for territorial species

Advances in field techniques have lead to an increase in spatially-referenced capture-recapture data to estimate a species' population size as well as other demographic parameters and patterns of space usage. Statistical models for these data have assumed that the number of individuals in the population and their spatial locations follow a homogeneous Poisson point process model, which implies that the individuals are uniformly and independently distributed over the spatial domain of interest. In many applications there is reason to question independence, for example when species display territorial behavior. In this paper, we propose a new statistical model which allows for dependence between locations to account for avoidance or territorial behavior. We show via a simulation study that accounting for this can improve population size estimates. The method is illustrated using a case study of small mammal trapping data to estimate avoidance and population density of adult female field voles (Microtus agrestis) in northern England

Characteristic and necessary minutiae in fingerprints

Fingerprints feature a ridge pattern with moderately varying ridge frequency (RF), following an orientation field (OF), which usually features some singularities. Additionally at some points, called minutiae, ridge lines end or fork and this point pattern is usually used for fingerprint identification and authentication. Whenever the OF features divergent ridge lines (e.g., near singularities), a nearly constant RF necessitates the generation of more ridge lines, originating at minutiae. We call these the necessary minutiae. It turns out that fingerprints feature additional minutiae which occur at rather arbitrary locations. We call these the random minutiae or, since they may convey fingerprint individuality beyond the OF, the characteristic minutiae. In consequence, the minutiae point pattern is assumed to be a realization of the superposition of two stochastic point processes: a Strauss point process (whose activity function is given by the divergence field) with an additional hard core, and a homogeneous Poisson point process, modelling the necessary and the characteristic minutiae, respectively. We perform Bayesian inference using an Markov-Chain-Monte-Carlo (MCMC)-based minutiae separating algorithm (MiSeal). In simulations, it provides good mixing and good estimation of underlying parameters. In application to fingerprints, we can separate the two minutiae patterns and verify by example of two different prints with similar OF that characteristic minutiae convey fingerprint individuality

Bayesian Repulsive Mixture Modeling with Mat\'ern Point Processes

Mixture models are a standard tool in statistical analysis, widely used for density modeling and model-based clustering. Current approaches typically model the parameters of the mixture components as independent variables. This can result in overlapping or poorly separated clusters when either the number of clusters or the form of the mixture components is misspecified. Such model misspecification can undermine the interpretability and simplicity of these mixture models. To address this problem, we propose a Bayesian mixture model with repulsion between mixture components. The repulsion is induced by a generalized Mat\'ern type-III repulsive point process model, obtained through a dependent sequential thinning scheme on a primary Poisson point process. We derive a novel and efficient Gibbs sampler for posterior inference, and demonstrate the utility of the proposed method on a number of synthetic and real-world problems

N-fold way simulated tempering for pairwise interaction point processes

Pairwise interaction point processes with strong interaction are usually difficult to sample. We discuss how Besag lattice processes can be used in a simulated tempering MCMC scheme to help with the simulation of such processes. We show how the N-fold way algorithm can be used to sample the lattice processes efficiently and introduce the N-fold way algorithm into our simulated tempering scheme. To calibrate the simulated tempering scheme we use the Wang-Landau algorithm