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SUMMARY:Inference for nonlinear dynamical systems\, with applications to t
 he ecology of infectious diseases. - Ed Ionides\, University of Michigan\,
  USA.
DTSTART:20071114T160000Z
DTEND:20071114T170000Z
UID:TALK9187@talks.cam.ac.uk
CONTACT:Dr. Leah R Johnson
DESCRIPTION:Nonlinear stochastic dynamical models are used to study ecolog
 ical systems and many other systems occuring across the sciences and engin
 eering. Such models are natural to formulate and can be analyzed mathemati
 cally and numerically. However\, difficulties associated with inference fr
 om time-series data about unknown parameters in these models have been a c
 onstraint on their application. We present a new method that makes maximum
  likelihood estimation feasible for partially-observed nonlinear stochasti
 c dynamical systems (also known as state-space models) where this was not 
 previously the case. The method is based on a sequence of filtering operat
 ions which are shown to converge to a maximum likelihood parameter estimat
 e. We make use of recent advances in nonlinear filtering in the implementa
 tion of the algorithm. We apply the method to the study of cholera in Bang
 ladesh. We construct confidence intervals\, perform residual analysis\, an
 d apply other diagnostics. Our analysis\, based upon a model capturing the
  intrinsic nonlinear dynamics of the system\, reveals some effects overloo
 ked by previous studies. 
LOCATION:Center for Mathematical Sciences\, MR 4
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