By Solomon Kullback
Hugely priceless textual content stories the logarithmic measures of knowledge and their software to checking out statistical hypotheses. themes contain advent and definition of measures of knowledge, their dating to Fisher’s details degree and sufficiency, primary inequalities of data concept, even more. a variety of labored examples and difficulties. References. word list. Appendix. 1968 moment, revised variation.
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2. A ﬁnite set E of exhaustive and mutually exclusive uncertain events or states of nature e1 , e2 , . . , en : only one of them will occur. 3. A set C of rewards cij , which are the consequences of having taken decision di when event ej occurs. The probabilities of the events E can also depend upon your decision, so that your probability pij of ej given decision di can be different from your probability pkj of the same event given another decision dk . You are supposed to follow a rational policy for assigning degrees of belief to states of nature, so that each feasible decision is a ‘gamble’ di = (ci 1 , .
25). If your preferences fail to satisfy any one of the axioms, then they cannot be represented by such a numerical function. But why, or in which cases, should your preferences fail? One must keep in mind that the preference ordering on the set G of ‘gambles’ is constructed starting from a given decision problem, with sets D, E , and C which are relative to that problem: this means that your utility function U is always relative to that framework. In a sense, the Ramsey–von Neumann–Morgenstern utility function U is context-dependent and it is signiﬁcantly different from Bernoulli’s ‘utility’ and from the concept of ‘utility’ held by nineteenth century philosophers and economists.
In a sense, the Ramsey–von Neumann–Morgenstern utility function U is context-dependent and it is signiﬁcantly different from Bernoulli’s ‘utility’ and from the concept of ‘utility’ held by nineteenth century philosophers and economists. e. that they are risk averters: a utility function inversely proportional to the decision maker’s total income is now only one of the possible shapes of the utility function U , when consequences are monetary rewards. The actual shape of your function U relative to a given decision problem will be revealed by your choices among gambles which are combinations of the rewards in that decision problem.