Bayesian hot spot detection in the presence of a spatial trend: application to total nitrogen concentration in Chesapeake Bay

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Abstract
Extreme concentrations of water quality variables can cause serious adverse effects in an ecosystem, making their detection an important environmental issue. In Chesapeake Bay, a decreasing gradient oftotal nitrogen concentrationextends from the highest values in the north at the mouth of the Susquehanna river to the lowest values in the south near the Atlantic ocean. We propose a general definition of ‘hot spot’ that includes previous definitions and is appealing for processes with a spatial trend. We model these data using the Bayesian Transformed Gaussian (BTG) random field model proposed by De Oliveiraet al. (1997), which combines the Box–Cox family of power transformations and a spatial trend. The median function is used as the measure of spatial trend, which offers some advantages over the customarily used mean function. The BTG model is fitted by an enhanced Monte Carlo algorithm, and the methodology is applied to the nitrogen concentration data. Copyright © 2002 John Wiley & Sons, Ltd.