Originally trained as a mathematician specializing in probability theory and stochastic processes, I was drawn to statistics by the interplay between theoretical and applied research- with new applications suggesting what statistical areas need theoretical development, and advances in theory and methodology suggesting what applications were becoming practical and so interesting. Through all of my statistical interests (theoretical, applied, and methodological) runs the unifying theme of the Likelihood Principle, a constant aid in the search for sensible methods of inference in complex statistical problems where commonly-used methods seem unsuitable. Three specific examples of such areas are:
Many of the methods in common use in each of these areas are hard or impossible to justify, and can lead to very odd inferences that seem to misrepresent the statistical evidence. Many of the newer approaches abandon the ``iid'' paradigm in order to reflect patterns of regional variation, and abandon familiar (e.g. Gaussian) distributions in order to reflect the heavier tails observed in realistic data, and nearly all of them depend on recent advances in the power of computer hardware and algorithms, leading to three other areas of interest:
I have a special interest in developing statistical methods for application to problems in Environmental Science, where traditional methods often fail. Recent examples include developing new and better ways to estimate the mortality to birds and bats from encounters with wind turbines; the development of nonexchangeable hierarchical Bayesian models for synthesizing evidence about the health effects of environmental pollutants; and the use of high-dimensional Bayesian models to reflect uncertainty in mechanistic environmental simulation models.
My current (2019) research involves modelling and Bayesian inference of dependent time series and (continuous-time) stochastic processes with jumps (examples include work loads on networks of digital devices; peak heights in mass spectrometry experiments; or multiple pollutant levels at spatially and temporally distributed sites), the theory & practice of Bayesian synthesis of evidence & information, Uncertainty Quantification and stochastic modeling in cosmology & astronomy (Gamma ray bursts, exoplanet detection, gravity waves) and high-energy physics (relativistic heavy ion collisions, jet quenching), and the statistical modelling of hazard and risk from, e.g., volcanic eruption.