Bayesian Semiparametric Intensity Estimation for Inhomogeneous Spatial Point Processes
Version of Record online: 22 DEC 2010
© 2010, The International Biometric Society
Volume 67, Issue 3, pages 937–946, September 2011
How to Cite
Yue, Y. R. and Loh, J. M. (2011), Bayesian Semiparametric Intensity Estimation for Inhomogeneous Spatial Point Processes. Biometrics, 67: 937–946. doi: 10.1111/j.1541-0420.2010.01531.x
- Issue online: 14 SEP 2011
- Version of Record online: 22 DEC 2010
- Received January 2010. Revised August 2010. Accepted August 2010.
- Adaptive spatial smoothing;
- Gaussian Markov random fields;
- Gibbs sampling;
- Intensity estimation;
- Spatial point process
Summary In this work we propose a fully Bayesian semiparametric method to estimate the intensity of an inhomogeneous spatial point process. The basic idea is to first convert intensity estimation into a Poisson regression setting via binning data points on a regular grid, and then model the log intensity semiparametrically using an adaptive version of Gaussian Markov random fields to smooth the corresponding counts. The inference is carried by an efficient Markov chain Monte Carlo simulation algorithm. Compared to existing methods for intensity estimation, for example, parametric modeling and kernel smoothing, the proposed estimator not only provides inference regarding the dependence of the intensity function on possible covariates, but also uses information from the data to adaptively determine the amount of smoothing at the local level. The effectiveness of using our method is demonstrated through simulation studies and an application to a rainforest dataset.