Bayesian Nonparametric Spatially Smoothed Density Estimation
A Bayesian nonparametric density estimator that changes smoothly in space is developed. The estimator is built using the predictive rule from a marginalized Polya tree, modified so that observations are spatially weighted by their distance from the location of interest. A simple refinement is proposed to accommodate arbitrarily censored data and a test for whether the density is spatially varying is also developed. The method is illustrated on two real datasets, and an R function SpatDensReg is provided for general use.
- Fisher, R. (1935). The design of experiments. Edinburgh: Oliver & Boyd.Google Scholar
- Gelfand A. E., Diggle, P. J., Fuentes, M., & Guttorp, P. (Eds.) (2010). Handbook of spatial statistics. Chapman&Hall/CRC handbooks of modern statistical methods. Boca Raton: CRC Press.Google Scholar
- MacEachern, S. N. (2001). Decision theoretic aspects of dependent nonparametric processes. In E. George (Ed.), Bayesian methods with applications to science, policy and official statistics (pp. 551–560). Luxembourg City: Eurostat.Google Scholar
- Zhou, H., & Hanson, T. (2018). spBayesSurv : Bayesian Modeling and Analysis of Spatially Correlated Survival Data. R package version 1.1.3 or higher. http://CRAN.R-project.org/package=spBayesSurv