Journal article
Multivariate spatial nonparametric modelling via kernel processes mixing
Statistica Sinica, Vol.23(1), pp.75-97
11/2013
DOI: 10.5705/ss.2011.172
PMCID: PMC3858969
PMID: 24347994
Abstract
In this paper we develop a nonparametric multivariate spatial model that avoids specifying a Gaussian distribution for spatial random effects. Our nonparametric model extends the stick-breaking (SB) prior of Sethuraman (1994), that is frequently used in Bayesian modelling to capture uncertainty in the parametric form of an outcome. The stick-breaking prior is extended here to the spatial setting by assigning each location a different, unknown distribution, and smoothing the distributions in space with a series of space-dependent kernel functions that have a space-varying bandwidth parameter. This results in a flexible nonstationary spatial model, as different kernel functions lead to different relationships between the distributions at nearby locations. This approach is the first to allow both the probabilities and the point mass values of the SB prior to depend on space. Thus, there is no need for replications and we obtain a continuous process in the limit. We extend the model to the multivariate setting by having, for each process, a different kernel function, but sharing the location of the kernel knots across the different processes. The resulting covariance for the multivariate process is in general nonstationary and nonseparable. The modelling framework proposed here is also computationally efficient because it avoids inverting large matrices and calculating determinants. We study the theoretical properties of the proposed multivariate spatial process. The methods are illustrated using simulated examples and an air pollution application to model components of fine particulate matter.
Details
- Title: Subtitle
- Multivariate spatial nonparametric modelling via kernel processes mixing
- Creators
- Montserrat Fuentes - North Carolina State UniversityBrian Reich
- Resource Type
- Journal article
- Publication Details
- Statistica Sinica, Vol.23(1), pp.75-97
- DOI
- 10.5705/ss.2011.172
- PMID
- 24347994
- PMCID
- PMC3858969
- NLM abbreviation
- Stat Sin
- ISSN
- 1017-0405
- eISSN
- 1996-8507
- Publisher
- Institute of Statistical Science, Academia Sinica and International Chinese Statistical Association
- Copyright
- 2013 © Institute of Statistical Science, Academia Sinica
- Language
- English
- Date published
- 11/2013
- Academic Unit
- Statistics and Actuarial Science; Biostatistics; Provost Office Administration
- Record Identifier
- 9983763482202771
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