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Thursday, May 17
Bayesian Modeling
Thu, May 17, 3:00 PM - 3:45 PM
Regency Ballroom B
 

Bayesian Modeling of Non-Stationary, Univariate, Spatial Data (304463)

Karl Ellefsen, U.S. Geological Survey 
*Margaret Goldman, U.S. Geological Survey 
Bradley Van Gosen, U.S. Geological Survey 

Keywords: Bayesian hierarchical model, non-stationary, spatial data, earth science data sets

The application of Bayesian statistics to regional and continental-scale earth science data sets is motivated by several data sets that pertain to the entire conterminous United States—airborne measurements of soil radioactivity, measurements of chemical element concentrations in soils, and measurements of chemical element concentrations in stream sediments. Exploratory analysis of these data sets shows that the mean and the variance are non-stationary. Estimating both statistics is important because both help infer the geological and geochemical processes that caused the observed spatial distribution. However, all published statistical models for analyzing such data sets are based on the assumption of stationarity in the variance, so they have limited usefulness for our applications. Consequently, we generalized a Bayesian hierarchical model to account for non-stationarity.

The Bayesian hierarchical model comprises three sub-models. First, the data model relates measurements of a physical property to simulated measurements. This relation accounts for measurement error, for which the variance is estimated independently. Second, the process model relates the simulated measurements of the physical property to parameters that characterize both the mean and the variance of the simulated measurements. These parameters vary spatially throughout the region being analyzed. This variation accounts for the non-stationarity. Third, the prior model establishes probability distributions for the parameters in the process model.

We present an example of this Bayesian modeling applied to titanium concentrations in stream sediments of the coastal plain of the southeastern United States. The mean and the variance from the process model are presented as maps, which provide information about earth processes at regional spatial scales. Some areas with high variance have a high degree of geologic heterogeneity that is caused by different depositional types.