EFFICIENT CALCULATION OF FISHER INFORMATION MATRIX: MONTE CARLO APPROACH USING PRIOR INFORMATION
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The Fisher information matrix (FIM) is a critical quantity in several aspects of mathematical modeling, including input selection and con¯dence region calculation. Analytical determination of the FIM in a general setting, specially in nonlinear mod- els, may be di±cult or almost impossible due to intractable modeling requirements and/or intractable high-dimensional integration. To circumvent these di±culties, a Monte Carlo (MC) simulation-based technique, resampling algorithm, based on the values of log-likelihood function or its exact stochastic gradient computed by using a set of pseudo data vectors, is usually rec- ommended. The current work proposes an extension of the resampling algorithm in order to enhance the statistical qualities of the estimator of the FIM. This modi¯ed resampling algorithm is useful in those cases where the FIM has a structure with some elements being analytically known from prior information and the others being unknown. The estimator of the FIM, obtained by using the proposed algorithm, si- multaneously preserves the analytically known elements and reduces variances of the estimators of the unknown elements by capitalizing on information contained in the ii known elements. Numerical illustrations considered in this work show considerable improvement of the new FIM estimator (in the sense of mean-squared error reduction as well as variance reduction) based on the modi¯ed MC based resampling algorithm over the FIM estimator based on the current MC based resampling algorithm.