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Department of Mathematical Sciences

Seminar Archives

On this page you can find information about seminars in this and previous academic years, where available on the database.

Statistics Seminars: Stochastic Differential Mixed-Effects Models

Presented by Umberto Picchini, Department of Mathematical Sciences, Durham University

18 October 2010 15:15 in CM221

** This is a rescheduled seminar (previously set on 11 October)**

Stochastic differential equation models (SDEs) are an established tool to describe random continuous time processes. Biomedical experiments often imply repeated measurements on a series of experimental units (e.g. subjects) and individual differences can be represented by incorporating random parameters into a statistical model, whose realizations differ from unit to unit. Such statistical models are known as "mixed-effects" models. I will introduce a framework to modellize simultaneously variability between the observed individual trajectories via a mixed-effects model and randomness into dynamics of the individual trajectory via an SDE, thus providing a powerful modeling tool with immediate applications in biomedicine and pharmacokinetic/pharmacodynamic studies.
In most cases the likelihood function for such model is not available, and thus maximum likelihood estimation for the unknown parameters is not possible. I will propose a computationally fast approximated maximum likelihood procedure for the estimation of both the non-random parameters and the random effects. An application to neuronal data will be presented.

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