Elizabeth Eli Holmes
Research Scientist, NMFS
Affiliate faculty, SAFS, University of Washington
National Marine Fisheries Service
Northwest Fisheries Science Center
2745 Montlake Blvd E
Seattle, WA 98112
eli.holmes(.)noaa.gov
www.nwfsc.noaa.gov/eli.holmes
faculty.washington.edu/eeholmes
206.860.3369
206.860.3400 fax
My research since my graduate student days has been focused on parsimony in population models: what does it mean, how to define it, and how to cross-validate it. What do I mean by 'parsimony in population models'? Basically, I mean how simple of a model can one use for a particular purpose. For example, if you have a spatial question then you need a spatial model, but what if your question is non-spatial then when can you use a non-spatial model to approximate the spatial process?
My initial graduate work was on spatial population dynamics and specifically how spatial interaction fundamentally changes population dynamics and to what extent does it not fundamentally change populations dynamics. If it does fundamentally change dynamics, then how simple can that spatial model be? At what point can a uniform mixing model approximate the properties of a non-uniform mixing process? The papers "Is diffusion too simple?", "Basic epidemiological concepts in a spatial context", and "Running from trouble" were all exploring these ideas. I reviewed some of these ideas in "Partial differential equation models in ecology". Later I taught a graduate course on spatial dynamics which tried to bring all these ideas together. My post-graduate work was focused on an experimental study of metapopulation dynamics using mosquitoes. This was a huge perturbation experiment to test some ideas about how metapopulation dynamics should change in response to variability in the environment.
Since 1999, I have been working with the National Marine Fisheries Service. I currently work on stochastic population dynamics. I am trying formulate hypotheses about parsimonious descriptions for population processes. I think about general canonical forms for the statistical distributions that population monitoring data should come from. I think about it as, 'does there exist a f(data) ~ g(theta)' under broad conditions -- that is under plausible population processes. Finding such an f and proving that it is distributed with the canonical form g, is primarily what concerns me. Why do I think about such esoteric things? Because I think that the process that generates my data on an endangered species is unknowable and unestimateable in my lifetime, and that the data, in and of themselves, will give me little information about the underlying process.
There are a few reasonable approaches to this problem, as I see it in January 2006. One approach is to be a pure Bayesian, develop a complicated model, fit that to the data, and use some type of model averaging across the posterior. Bayesians argue that since you model average across the posterior this approach does not suffer from the data-mining problem faced in frequentist statistics when the number of parameters greatly outnumbers the number of data points. At the moment, my understanding of Bayesian statistics is not sufficiently deep to evaluate that argument. At the same time, I'm alarmed at the degree of data-mining/model-fudging that goes on in typical model-building. Bayesian approaches seem to be an improvement on that. The problem is that a) I have a hard time accepting vague priors especially in complex models with a gazillion parameters and b) we know a lot about population processes, and we should be able to come up with theoretically motivated informative priors.
My recent paper, "A statistical approach to quasi-extinction forecasting", is the culmination of two years of pondering on this problem. Having completed this however I am forcibly reminded of the quote that opens Bernt Oksendal's book Stochastic differential equations: "We have not succeeded in answering all our problems. The answers we have found only serve to raise a whole set of new questions. In some ways we feel we are as confused as ever, but we believe we are confused on a higher level and about more important things."