Ivanenko Decision Systems and Nonstochastic Randomness

1. Auflage 2010
ISBN: 978-1-4419-5548-7
Verlag: Springer US
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, 272 Seiten, Web PDF

"Decision Systems and Non-stochastic Randomness" is the first systematic presentation and mathematical formalization (including existence theorems) of the statistical regularities of non-stochastic randomness. The results presented in this book extend the capabilities of probability theory by providing mathematical techniques that allow for the description of uncertain events that do not fit standard stochastic models.
The book demonstrates how non-stochastic regularities can be incorporated into decision theory and information theory, offering an alternative to the subjective probability approach to uncertainty and the unified approach to the measurement of information.
This book is intended for statisticians, mathematicians, engineers, economists or other researchers interested in non-stochastic modeling and decision theory.

Zielgruppe

Research

Autoren/Hrsg.

Ivanenko, V. I.

Inhaltsverzeichnis

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.

Leseproben

"Chapter 2 Decision Systems (p. 19-20)

The correct statement of the laws of physics involves some very unfamiliar ideas which require advanced mathematics for their description. Therefore one needs a considerable amount of preparatory training even to learn what the words mean.
Richard Feynman

2.1 Preliminaries

Decision theory emerged from the requirements of diverse fields of human activity such as medicine, gambling, politics, warfare, economics and finance, and engineering. Perhaps this is the reason for the terminological diversity that sometimes impedes not only mutual understanding between specialists in different fields but also the development of decision theory itself. In this sense, control theory has been more fortunate, for its terminology turned out to be common to many spheres of its application.

There are two points of view on the relationship between decision theory and control theory. According to one such view, they have nothing in common. According to the other, these theories are gradually converging because the differences between them are not fundamental [14, 18]. The author of this book is an adherent of the latter viewpoint, and proposes the following motivation. In control theory one studies a control system that consists of a pair of objects: a plant and a controller. In decision theory one studies a pair consisting of a decision situation and a decision-maker. It is natural to call such a pair a decision system. A control system is defined similarly.

The problem of choice of a decision or a control—an action that produces some consequence—is a problem common to both systems. In both systems, one may encounter two basic difficulties in the process of making this choice: dynamics and uncertainty. The development of control theory began in engineering, and the dynamics of plants became its central problem. The development of decision theory began in economics, and uncertainty became its central problem. While this dichotomy still exists, more and more attention is now being devoted to uncertainty in control theory [53] and to dynamics in decision theory [14].

But there is still an essential difference. Whereas the choice of decision criterion is at the center of decision theory, it is still on the periphery in control theory. A systematic mathematical study of a control system becomes possible only if we define mathematical models of its components: the controlled plant, the controller, and the experiment (observation) the controller can perform over the plant. The same must be true about a decision system.

Therefore, in this chapter we introduce the notion of a decision system and mathematical models of its components: the decision situation, the decision-maker, and the experiment (observation) the decision-maker can perform over the decision situation. An attempt to define a model of the second component of a decision system (the decision-maker) may seem surprising if we do not mention that our model concerns only the sequence of specific operations any decision-maker performs in the process of decision-making."