Decision Systems and Nonstochastic Randomness - Ivanenko, V. I.; SpringerLink (Online service) (New York, NY : Springer New York, 2010)
(3z(BDecision Systems and Nonstochastic Randomness(3y (Bpresents the first mathematical formalization of the statistical regularities of non-stochastic randomness and demonstrates how these regularities extend the standard probability-based model of decision making under uncertainty, allowing for the description of uncertain mass events that do not fit standard stochastic models. Each self-contained chapter of this neatly-structured monograph includes a detailed introduction and summary of its contents. The included results are presented not only with rigorous proofs but also through numerous intuitive examples. An appendix is provided which includes classic results from the theory of functions and measured sets as well as decision theory, offering an overview of the necessary prerequisites. The formalism of statistical regularities developed in this book will have a significant influence on decision theory and information theory as well as numerous other disciplines. Because of these far-reaching implications, this book may be a useful resource for statisticians, mathematicians, engineers, economists and other utilizing nonstochastic modeling and decision theory.s
Decision Systems -- Indifferent Uncertainty -- Nonstochastic Randomness -- General Decision Problems -- Experiment in Decision Problems -- Informativity of Experiment in Bayesian Decision Problems -- Reducibility of Experiments in Multistep Decision Problems -- Concluding Remarks.
Keywords: Mathematics; Distribution (Probability theory).; Mathematical statistics; Economics -- Statistics; Mathematics; Probability Theory and Stochastic Processes; Statistical Theory and Methods; Game Theory, Economics, Social and Behav. Sciences; Operations Research/Decision Theory; Statistics for Business/Economics/Mathematical Finance/Insurance.