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.

Effective Thermal Conductivity Estimates Of Particulate Mixtures

Several theories have been advanced to estimate effective thermal conductivities of particulate mixtures, but most theories have focused on the dilute case. A method is proposed to estimate the effective thermal conductivity coefficient of mixtures of arbitrary concentration. Earlier the authors developed a theory to determine the expected contact area between different species. This theory is employed to determine the Kapitza resistance of the heterogeneous mixture and forms part of an overall theory to estimate the effective thermal conductivity. Results are compared with other theoretical estimates and with experiments.