The Bernstein-von Mises theorem and spectral asymptotics of Bayes estimators for parabolic SPDEs
The Bernstein-von Mises theorem and spectral asymptotics of Bayes estimators for parabolic SPDEs
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抛物线 SPDE 的 Bernstein-von Mises 定理和贝叶斯估计量的谱渐近
DOI：
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发表时间：
2002
影响因子：
0.7
通讯作者：
J. Bishwal
中科院分区：
文献类型：
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作者：
J. Bishwal
证明了一类线性参数抛物型随机偏微分方程解的傅立叶系数个数增加到无穷大时，关于适当归一化和中心的后验密度收敛到正态密度的Bernstein-von Mose定理.结果表明，对于光滑损失函数和先验分布，漂移参数的Bayes估计是强相合的、渐近正态的和局部渐近极小的(在Hajek-Le Cam意义下)，并且当傅立叶系数的个数变大时，它与最大似然估计渐近等价。与经典的有限维随机微分方程不同，这里的总观测时间和噪声强度保持不变。
Abstract The Bernstein-von Mises theorem, concerning the convergence of suitably normalized and centred posterior density to normal density, is proved for a certain class of linearly parametrized parabolic stochastic partial differential equations (SPDEs) as the number of Fourier coefficients in the expansion of the solution increases to infinity. As a consequence, the Bayes estimators of the drift parameter, for smooth loss functions and priors, are shown to be strongly consistent, asymptotically normal and locally asymptotically minimax (in the Hajek-Le Cam sense), and asymptotically equivalent to the maximum likelihood estimator as the number of Fourier coefficients become large. Unlike in the classical finite dimensional SDEs, here the total observation time and the intensity of noise remain fixed.