Seminar in applied mathematics and statistics

SPEAKER: Subhash R. Lele (University of Alberta)

TITLE: Confronting perfect models with imperfect data using data cloning
(A.K.A. How to trick Bayesians into giving frequentist answers)

ABSTRACT:
Hierarchical models have found applications in numerous fields. These models arise as a way to complex natural processes involving various interacting systems; they arise because there is missing data, detection error, measurement error in covariates and so on. The Generalized Linear Mixed Models (GLMM) is an important class of models. Likelihood function for these models, however, is nearly impossible to write analytically. Bayesian inference, especially using the non-informative priors and MCMC, is the de facto method currently used in practice. In this talk, I will discuss how a small modification to the MCMC procedure can provide us with the frequentist inferential statements. Aside from being able to obtain the MLE, this method also has some additional important features: (1) It automatically leads to an estimate of the asymptotic variance, (2) It automatically lets the user know whether the parameters of the model are estimable or not, (3) It can be used with any likelihood type objects (estimating functions, conditional likelihood, composite likelihood etc.), and (4) It is possible to get the profile likelihood inference for the parameter of interest. I will discuss the method and the underlying statistical theory. I will illustrate its use in some conservation biology situations and contrast it with the Bayesian inference with non-informative priors.

Tea and chocolate will be served in room 04.3.15 after the seminar.