2005/11/11 by James C. Spall · 2 citations
Decision Sciences · Mathematics · #Probabilistic and Robust Engineering Design #Simulation Techniques and Applications #Statistical Distribution Estimation and Applications #Fisher information #Hessian matrix #Resampling #Prior probability #Mathematical optimization #Computer science #Algorithm #Matrix (chemical analysis) #Monte Carlo method #Computation #Mathematics #Applied mathematics #Bayesian probability #Artificial intelligence #Statistics #Machine learning
paper · doi:10.1198/106186005x78800
openalex publication_date 2005/11/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/29
The Fisher information matrix summarizes the amount of information in the data relative to the quantities of interest. There are many applications of the information matrix in modeling, systems analysis, and estimation, including confidence region calculation, input design, prediction bounds, and “noninformative” priors for Bayesian analysis. This article reviews some basic principles associated with the information matrix, presents a resampling-based method for computing the information matrix together with some new theory related to efficient implementation, and presents some numerical results. The resampling-based method relies on an efficient technique for estimating the Hessian matrix, introduced as part of the adaptive (“second-order”) form of the simultaneous perturbation stochastic approximation (SPSA) optimization algorithm.