Efficient Monte Carlo computation of Fisher information matrix using prior information

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, especially 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, known as resampling algorithm, is usually recommended, in which values of the log-likelihood function or its exact stochastic gradient computed based on a set of pseudo-data vectors are used. 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 on the information contained in the known elements.