Efficient Monte Carlo Computation of Fisher Information Matrix using Prior Information
Sonjoy Das, James C. Spall and Roger Ghanem
Computational Statistics and Data Analysis, v , No , pp. -- , 2009, doi:
The Fisher information matrix (FIM) is a critical quantity in several aspects of
mathematical modeling, including input selection and confidence region
calculation. Analytical determination of the FIM in a general setting, specially
in nonlinear models, may be difficult or almost impossible due to intractable
modeling requirements or/and intractable high-dimensional integration.
To circumvent these difficulties, a Monte Carlo simulation-based technique,
resampling algorithm, based on values of the associated log-likelihood function
or its exact stochastic gradient computed by using a set of pseudo data vectors,
is usually recommended. The current work proposes an extension of this
resampling algorithm in order to enhance the statistical qualities of the
estimator of the FIM. This modified resampling algorithm is useful in those
cases when some elements of the FIM are analytically known from prior
information and the rest of the elements are unknown. The estimator of the FIM
resulting from the proposed algorithm simultaneously preserves the analytically
known elements and reduces variances of the estimators of the unknown elements.
This is achieved by capitalizing the information contained in the known
elements.
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