4 citations · 6 across the 6 of their papers we have counts for
8 papers
The partial K function
Jake P. Grainger, Tuomas A. Rajala, David J. Murrell +1
The K function and its related statistics have been an enduring tool in the analysis of spatial point processes, providing an easy to compute and interpret summary statistic for ch…
Spectral estimation for spatial point processes and random fields
Jake P. Grainger, Tuomas A. Rajala, David J. Murrell +1
Spatial variables can be observed in many different forms, such as regularly sampled random fields (lattice data), point processes, and randomly sampled spatial processes. Joint an…
Visualizing the Wavenumber Content of a Point Pattern
Jake P. Grainger, Tuomas A. Rajala, David J. Murrell +1
Spatial point patterns are a commonly recorded form of data in ecology, medicine, astronomy, criminology, epidemiology and many other application fields. One way to understand thei…
What is the Fourier Transform of a Spatial Point Process?
Tuomas A. Rajala, Sofia C. Olhede, Jake P. Grainger +1
This paper determines how to define a discretely implemented Fourier transform when analysing an observed spatial point process. To develop this transform we answer four questions;…
When do we have the power to detect biological interactions in spatial point patterns?
T. Rajala, S. Olhede, D. J. Murrell
Determining the relative importance of environmental factors, biotic interactions and stochasticity in assembling and maintaining species-rich communities remains a major challenge…
A review on anisotropy analysis of spatial point patterns
Tuomas Rajala, Claudia Redenbach, Aila Särkkä +1
A spatial point pattern is called anisotropic if its spatial structure depends on direction. Several methods for anisotropy analysis have been introduced in the literature. In this…
Detecting multivariate interactions in spatial point patterns with Gibbs models and variable selection
Tuomas Rajala, David Murrell, Sofia Olhede
We propose a method for detecting significant interactions in very large multivariate spatial point patterns. This methodology develops high dimensional data understanding in the p…
A note on Bayesian logistic regression for spatial exponential family Gibbs point processes
Tuomas Rajala
Recently, a very attractive logistic regression inference method for exponential family Gibbs spatial point processes was introduced. We combined it with the technique of quadratic…