Bayesian inference for Matérn repulsive processes
In many applications involving point pattern data, the Poisson process assumption is unrealistic, with the data exhibiting a more regular spread. Such repulsion between events is exhibited by trees for example, because of competition for light and nutrients. Other examples include the locations of biological cells and cities, and the times of neuronal spikes. Given the many applications of repulsive point processes, there is a surprisingly limited literature developing flexible, realistic and interpretable models, as well as efficient inferential methods. We address this gap by developing a modelling framework around the Matérn type III repulsive process. We consider some extensions of the original Matérn type III process for both the homogeneous and the inhomogeneous cases. We also derive the probability density of this generalized Matérn process, allowing us to characterize the conditional distribution of the various latent variables, and leading to a novel and efficient Markov chain Monte Carlo algorithm. We apply our ideas to data sets of spatial locations of trees, nerve fibre cells and Greyhound bus stations.
Duke Scholars
Published In
DOI
EISSN
ISSN
Publication Date
Volume
Issue
Start / End Page
Related Subject Headings
- Statistics & Probability
- 4905 Statistics
- 3802 Econometrics
- 1403 Econometrics
- 0104 Statistics
- 0102 Applied Mathematics
Citation
Published In
DOI
EISSN
ISSN
Publication Date
Volume
Issue
Start / End Page
Related Subject Headings
- Statistics & Probability
- 4905 Statistics
- 3802 Econometrics
- 1403 Econometrics
- 0104 Statistics
- 0102 Applied Mathematics