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\noindent Statistica Sinica {\bf 13}(2003), 255-274
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\centerline{\large\bf POSTERIOR MODE ESTIMATION FOR NONLINEAR}
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\centerline{\large\bf AND NON-GAUSSIAN STATE SPACE MODELS}
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\centerline{Mike K. P. So}
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\centerline{\it Hong Kong University of Science and Technology}
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\begin{quotation}
\noindent {\it Abstract:}
In this paper, we develop a posterior mode estimation method
for nonlinear and non-Gaussian state space models. By exploiting special
structures of the state space models, we derive a modified quadratic
hill-climbing procedure which can be implemented efficiently in O($n$)
operations. The method can be used for estimating the state variable,
performing Bayesian inference and carrying out Monte Carlo likelihood
inference. Numerical illustrations using simulated and real data demonstrate
that our procedure is much more efficient than a common gradient method.  It
is also evident that our method works very well in a new stochastic volatility
model which contains a nonlinear state equation.\par
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\noindent {\it Key words and phrases:}
Filtering, Kalman filter, quadratic hill-climbing,
stochastic volatility model, time series.
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