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Download PDF by José M. Bernardo, Adrian F. M. Smith: Bayesian Theory

By José M. Bernardo, Adrian F. M. Smith

ISBN-10: 047149464X

ISBN-13: 9780471494645

This hugely acclaimed textual content offers a radical account of key suggestions and theoretical effects, with specific emphasis on viewing statistical inference as a different case of selection concept.
Information-theoretic suggestions play a critical function within the improvement of the speculation, which supplies, particularly, a close dialogue of the matter of specification of so-called previous lack of know-how.

The paintings is written from the authors' devoted Bayesian standpoint, yet an summary of non-Bayesian theories is usually supplied, and every bankruptcy includes a wide-ranging severe re-evaluation of arguable concerns. the extent of arithmetic used is such that almost all fabric is on the market to readers with wisdom of complex calculus. particularly, no wisdom of summary degree idea is thought, and the emphasis all through is on statistical options instead of rigorous mathematics.

The e-book can be an awesome resource for all scholars and researchers in records, arithmetic, determination research, financial and company reviews, and all branches of technological know-how and engineering, who desire to additional their realizing of Bayesian information.

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Extra info for Bayesian Theory

Example text

In such cases, the decision problem can be represented schematically by means of a decision tree as shown in Figure 2. I . 1 Decision tree The square represents a decision node, where the choice of an action is required. The circle represents an uncertainty node where the outcome is beyond our control. Following the choice of an action and the occurrence of a particular event, the branch leads us to the corresponding consequence. 6, these reduce, essentially, to repeated analyses based on the above structure.

That G 5 (3. thus contradicting C: > k!. Hence. by Axiom I(ii). ('1 5 ( ' 2 . , if E E F , then F cannot be considered less likely than E . 4. (Monotonicity). I f E 5 F then E 5 F. Proof. For any c1 < CZ. define a1 = { Q I E,cl I E'} = {CI 1 F - E , {CZ I E,CI1 E"} I ( F - E ) " } , = {Q I F , c ~ IF"} = {CZ IF - Ey { ~ IE:cI 2 I E"} I ( F - E ) " } . 2 that E 5 F. n E", al 5 a2. It now follows immediately This last result is an example of how coherent qualitative comparisons of uncertain events in terms of the "not more likely" relation conform to intuitive requirements.

I b'. 2. This forrnalises the intuitive idea that the stated preference should only depend on the "relative likelihood" of F-' and E' and should not depend on the particular consequences used in constructing the options. Similarly. (iii) asserts that if we have the preference { ( I , I G'. (. i G' } i { (12 I C. c I G"}for some c then. given C;. ( 1 1 should not be preferred to (12. so that. for any u. { (1 I 1 G, (I I C" } 5 { I G. ( 1 1 C ' } ,This latter argument is a version of what might be called the sure-thing principle: if two situations are such that whatever the outcome of the first there is a preferable corresponding outcome of the second, then the second situation is preferable overall.

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Bayesian Theory by José M. Bernardo, Adrian F. M. Smith


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