77 research outputs found
Local likelihood estimation for covariance functions with spatially-varying parameters: the convoSPAT package for R
In spite of the interest in and appeal of convolution-based approaches for
nonstationary spatial modeling, off-the-shelf software for model fitting does
not as of yet exist. Convolution-based models are highly flexible yet
notoriously difficult to fit, even with relatively small data sets. The general
lack of pre-packaged options for model fitting makes it difficult to compare
new methodology in nonstationary modeling with other existing methods, and as a
result most new models are simply compared to stationary models. Using a
convolution-based approach, we present a new nonstationary covariance function
for spatial Gaussian process models that allows for efficient computing in two
ways: first, by representing the spatially-varying parameters via a discrete
mixture or "mixture component" model, and second, by estimating the mixture
component parameters through a local likelihood approach. In order to make
computation for a convolution-based nonstationary spatial model readily
available, this paper also presents and describes the convoSPAT package for R.
The nonstationary model is fit to both a synthetic data set and a real data
application involving annual precipitation to demonstrate the capabilities of
the package
Accounting for Uncertainty in Ecological Analysis: The Strengths and Limitations of Hierarchical Statistical Modeling
Copyright by the Ecological Society of America.Analyses of ecological data should account for the uncertainty in the process(es) that generated the data. However, accounting for these uncertainties is a difficult task, since
ecology is known for its complexity. Measurement and/or process errors are often the only sources of uncertainty modeled when addressing complex ecological problems, yet analyses should also account for uncertainty in sampling design, in model specification, in parameters governing the specified model, and in initial and boundary conditions. Only then can we be confident in the scientific inferences and forecasts made from an analysis. Probability and statistics provide a framework that accounts for multiple sources of uncertainty. Given the complexities of ecological studies, the hierarchical statistical model is an invaluable tool. This
approach is not new in ecology, and there are many examples (both Bayesian and non-Bayesian)
in the literature illustrating the benefits of this approach. In this article, we provide a baseline for concepts, notation, and methods, from which discussion on hierarchical statistical modeling in ecology can proceed. We have also planted some seeds for discussion and tried to show where the practical difficulties lie. Our thesis is that hierarchical statistical modeling is a powerful way of approaching ecological analysis in the presence of inevitable but quantifiable uncertainties, even if practical issues sometimes require pragmatic compromises
Accounting for uncertainty in ecological analysis: the strengths and limitations of hierarchical statistical modeling
Analyses of ecological data should account for the uncertainty in the process(es) that generated the data. However, accounting for these uncertainties is a difficult task, since ecology is known for its complexity. Measurement and/or process errors are often the only sources of uncertainty modeled when addressing complex ecological problems, yet analyses should also account for uncertainty in sampling design, in model specification, in parameters governing the specified model, and in initial and boundary conditions. Only then can we be confident in the scientific inferences and forecasts made from an analysis. Probability and statistics provide a framework that accounts for multiple sources of uncertainty. Given the complexities of ecological studies, the hierarchical statistical model is an invaluable tool. This approach is not new in ecology, and there are many examples (both Bayesian and non-Bayesian) in the literature illustrating the benefits of this approach. In this article, we provide a baseline for concepts, notation, and methods, from which discussion on hierarchical statistical modeling in ecology can proceed. We have also planted some seeds for discussion and tried to show where the practical difficulties lie. Our thesis is that hierarchical statistical modeling is a powerful way of approaching ecological analysis in the presence of inevitable but quantifiable uncertainties, even if practical issues sometimes require pragmatic compromises
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