|I have many areas of research interest within Statistics and Operations Research, including both application and theoretical development.
Recent work has focused on estimating the total numbers of species of different taxa, which has been joint work with Simon Wilson of Trinity College and Mark Costello of the Leigh Marine Laboratory, University of Auckland. Currently this is based on data from the dates of first reporting of different species, starting with the initial work of Linnaeus. This question is important in discussion of species extinction rates and biodiversity. We form part of a global team, including researchers in Canada, France, the United States and Australia, that is evaluating the many different methods of estimating species numbers.
I have a strong interest in the foundations of statistics, and specifically, normative Bayesian statistical decision theory, with previous work in this area focusing on the generalisation of adaptive utility that permits uncertainty in not only a decision maker's beliefs, but also their preferences. A brief outline of work conducted in this area is summarised:
Theories of sequential decision making have been developed to consider coherent decision making strategies over several decision epochs when actual decision outcomes are a priori uncertain. Such theories have many areas of application, e.g., experimental design and policy development, with contributions being made by researchers in mathematics, statistics, economics, philosophy and psychology.
Traditionally, all uncertainties are modelled via precise probabilities, and all preferences over decision outcomes via known utilities. It is recognised, however, that indeterminacy may complicate assessment of such probabilities and/or utilities, especially when the decision maker has little or no prior experience within the context of the decision problem under consideration. As such, recent attention has focused on developing decision making algorithms that are able to accommodate imprecise probabilities (where precise values are replaced by intervals) and/or uncertain utilities (where fixed quantities are replaced by random variables). This then allows indeterminacy to be taken into account, generalising classical theories of decision making, and permitting the creation of robust Bayesian methods for within statistical decision theory. However, further implications are the effects these generalisations have on the axiomatic foundations of the theory, and also on traditional decision theory concepts such as value of information and risk aversion.
Finally, I also have a growing interest in the use of statistical arguments for policy development.