Spatial Statistics and Environmental Challenges

Alan Gelfand

The worlds of spatial statistics and of environmental modeling are both enormous. In a brief one hour lecture, it is not possible to cover much of this terrain. So, I will focus on two large problems which connect both of these areas: modeling of species distributions and modeling of environmental exposure. All of the modeling and inference will be done within the Bayesian framework. For the former, modeling of species distributions is a dominant question in ecology, understanding where species are and why. I will discuss modeling of data in the form of presence-absence as well as abundance. This context places us in the geostatistical realm, observing random responses at fixed sampling locations. In this regard, I will consider modeling species individually and jointly. Then, I will turn to presence-only sampling where the data now is more naturally viewed as a spatial point pattern, always degraded by sampling effort. Finally, here, I will try to shed light on the issue of fusion of presence-absence data with presence-only data over a common region. I will argue that much of the previous literature has handled this problem incorrectly and show that a preferential sampling perspective can yield a more satisfying story. For the second, there is continuing strong interest in describing exposure to environmental contaminants, particularly with concerns regarding their connection to adverse health outcomes. I will begin with the basic geostatistical modeling for environmental exposure both in space and in space-time. The simplest versions model pollutants individually or jointly using monitoring station data. However, these days we often supplement such data with data from computer models and/or remotely-sensed from satellites. This takes us to data fusion challenges with observations at different spatial scales. Finally, with the enormous growth in data collection, I will also discuss fully Bayesian approaches for handling big datasets in space and time.

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