Invited Session II Abstracts

Invited Session II: Recent Methodological Developments in Spatial Statistics

Friday, October 5, 10:45 a.m. – 12:45 p.m.

Session Chair: Petrutza Caragea

 

Some Reflections on the Theoretical Study in Spatial Statistics

Hao Zhang

The recent advances in infill asymptotic theory have resulted in computationally more efficient algorithms that yield statistical estimators as efficient as the maximum likelihood estimators. These results also bring about a deep understanding of what aspect of a spatial model that we should pay more attention to. I will review some of the results and discuss some open problems. 

 Analysis of Variance for Functional and Image Data, with Climate Applications

Marc G. Genton

 In Statistics, the analysis of variance (ANOVA) method is used to partition the observed variance of a particular variable into components attributable to different sources of variation. Traditional ANOVA models are fitted by sample means applied to univariate data. However, modern science problems often involve complex data structures, such as functional and image data, i.e. each observation is a temporal curve or a spatial surface rather than a single number. Such complex data arise in many fields, including meteorology, biology, environmetrics, medicine, and engineering.

 For example, in order to investigate sources of variability in the output of climate models where the factors are the choice of regional climate models (RCMs) and the choice of their boundary conditions from global circulations models (GCMs), each observation is an image. In this talk, we consider the extension of the classical ANOVA to functional and image data, and propose a robust fitting procedure coined functional median polish for one-way and two-way functional analysis of variance. The functional median polish estimates the functional grand effect and functional main factor effects with functional medians based on band depth in an additive functional ANOVA model assuming no interaction among factors. We propose a fast algorithm that allows to rank functions or images for large datasets. A functional rank test is used to assess whether the functional main factor effects are significant. The robustness of the functional median polish is demonstrated by comparing its performance with the functional ANOVA fitted by means under different outlier models in Monte Carlo simulation studies. The results are visualized with functional boxplots. The functional median polish is illustrated on various applications in climate science, including one-way and two-way ANOVA when functional data are either curves or images. Specifically, U.S. precipitation observations and outputs of global and regional climate models are considered.

 

Nonparametric Estimation of Spatial Covariance Function

Bo Li

Covariance structure modeling plays a key role in the spatial data analysis. Various parametric models have been developed to accommodate the idiosyncratic features of a given data set. However, the parametric modelsmay impose unjustified restrictions to the covariance structure and the procedure of choosing a specific model is often ad-hoc. To avoid thechoice of parametric forms, we propose a nonparametric covariance estimator for the spatial data, as well as its extension to the spatio-temporal data  based on the class of space-time covariance models developed by Gneiting (2002). Our estimator is obtained via a nonparametric approximation of completely monotone functions. It is easy to implement and our simulation shows it outperforms the parametric modelswhen there is no clear information on model specification. Two real data examples are analyzed to illustrate our approach and provide further comparison between the nonparametric estimator and parametric models.

 

 Multivariate Receptor Models for Spatially Correlated Multi-Pollutant Data

Mikyoung Jun and Eun Sug Park

 The goal of multivariate receptor modeling is to estimate the profiles of major pollution sources and quantify their impacts based on ambient measurements of pollutants. Traditionally, multivariate receptor modeling has been applied to multiple air pollutant data measured at a single monitoring site or measurements of a single pollutant collected at multiple monitoring sites. Despite the growing availability of multi-pollutant data collected from multiple monitoring sites, there has not yet been any attempt to incorporate spatial dependence that may exist in such data into multivariate receptor modeling. We propose a spatial statistics extension of multivariate receptor models that enables us to incorporate spatial dependence into estimation of source composition profiles and contributions given the pre-specified number of sources and the model identification conditions. The proposed method yields more precise estimates of source profiles by accounting for spatial dependence in the estimation. More importantly, it enables predictions of source contributions at unmonitored sites as well as when there are missing values at monitoring sites. The method is illustrated with  simulated data and real multi-pollutant data collected from 8 monitoring sites in Harris County, Texas.