Bayesian Estimations for Diagonalizable Bilinear SPDEs
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The main goal of this paper is to study the parameter estimation problem, using the Bayesian methodology, for the drift coefficient of some linear (parabolic) SPDEs driven by a multiplicative noise of special structure. We take the spectral approach by assuming that one path of the first N Fourier modes of the solution are continuously observed over a finite time interval. We derive Bayesian type estimators for the drift coefficient, and as custom for Bayesian statistics, we prove a Bernstein-Von Mises theorem for the posterior density. Consequently, we obtain some asymptotic properties of the proposed estimators, as N→∞. Finally, we present some numerical examples that illustrate the obtained theoretical results.
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