ENTROPY MINIMAX MULTIVARIATE STATISTICAL MODELING—II: APPLICATIONS

Abstract

Applications of entropy minimax are summarized in three major areas: meteorology, engineering/ materials science, and medicine/biology. The applications cover both discrete patterns in multidimensional spaces of mixed quantitative and qualitative variables, and continuous patterns employing concepts of potential functions and fuzzy entropies. Major achievements of entropy minimax modeling include the first long range weather forecasting models with statistical reliability significantly above chance verified on independent data, the first models of fission gas release and nuclear fuel failure under commercial operating conditions with significant and independently verified statistical reliability, and the first prognosis models in coronary artery disease and in non-Hodgkin's lymphoma with significant predictability verified on independent data. In addition, applications of entropy minimization and maximization separately are reviewed, including feature selection, unsupervised classification, probability estimation, statistical distribution determination, statistical mechanics and thermodynamics, pattern recognition, spectral analysis and image reconstruction. Comparisons between entropy minimax and other methodolodies are provided, including sample average predictors, nearest neighbors predictors, linear regression, logistic regression, Cox proportional hazards regression, recursive partitioning, linear discriminant analysis, mechanistic modeling, and expert (heuristic) programming.

INDEX TERMS:

• Cancer survival analysis
• crossvalidation
• data analysis
• diagnosis
• differential diagnosis
• entropy
• entropy minimax
• experimental design
• failure analysis
• feature selection
• fission gas release
• forecasting
• hazard analysis
• heart disease survival analysis
• information theory
• long range weather forecasting
• materials deformation
• maximum entropy
• medical diagnosis
• medical prognosis
• minimum entropy
• molecular evolution
• multivariale statistics
• nuclear fuel failure
• pattern discovery
• predictive modeling
• probability estimation
• statistical modeling
• statistical prediction
• survival analysis
• system failure
• systems modeling
• tank lifetime analysis
• underground storage system leakage
• weather forecasting
• weight normalization.

Additional information

Notes on contributors

RONALD CHRISTENSEN

Ronald Christensen has headed Entropy Limited, conducting statistical modeling research in science, engineering and medicine, since 1973. Previously, he held research positions at IBM, the RAND Corporation and the Lawrence Berkeley Laboratory. He has taught and conducted research at Carnegie-Mellon University, the University of Maine and the University of California, Berkeley, and is the author of General Description of Entropy Minimax, 1981, Multivariate Statistical Modeling, 1983, Order and Time, 1984, Data Distributions, 1984, and other books and papers in physics, statistics, and predictive modeling. Dr. Christensen received a Ph.D. in Theoretical Physics from the University of California, Berkeley, a J.D. from Harvard Law School, an M.S. in Mechanical Engineering from the California Institute of Technology, and a B.S. in Electrical Engineering from Iowa State University. He is a member of the American Mathematical Society, the American Statistical Association and the American Physical Society.