In many applications of interest, such as the conformational
dynamics of molecules, large deterministic systems can exhibit
stochastic behaviour in a relative small number of coarse-grained
variables. This kind of dimension reduction, from a large deterministic
system to a smaller stochastic one, can be very useful in understanding
the problem. Whilst the subject of statistical mechanics provides
a wealth of explicit examples where stochastic models for coarse
variables can be found analytically, it is frequently the case
that applications of interest are not amenable to analytic
dimension reduction. It is hence of interest to pursue computational
algorithms for such dimension reduction. This talk will be devoted
to describing recent work on parameter estimation aimed at
problems arising in this context.
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Joint work with Raz Kupferman (Jerusalem) and Petter Wiberg (Warwick)