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, model selection, and confidence region calculation. For example, the determinant of the FIM is the main performance metric for choosing input values in a scientific experiment with the aims of achieving the most accurate resulting parameter estimates in a mathematical model. However, analytical determination of the FIM in a general setting, especially in nonlinear models, may be difficult or almost impossible due to intractable modeling requirements and/or intractable high-dimensional integration.

To circumvent these difficulties, 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 recommended. This paper proposes an extension of the current algorithm in order to enhance the statistical characteristics of the estimator of the FIM. This modified algorithm is particularly 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, simultaneously preserves the analytically known elements and reduces the variances of the estimators of the unknown elements by capitalizing on the information contained in the known elements.