By Richard M. Cyert, Morris H. DeGroot (auth.)
We begun this study with the target of using Bayesian tools of study to numerous features of financial concept. We have been interested in the Bayesian procedure since it appeared the easiest analytic framework on hand for facing selection making lower than uncertainty, and the learn offered during this ebook has simply served to bolster our trust within the appropriateness and usability of this technique. extra specif ically, we think that the concept that of organizational studying is funda psychological to choice making lower than uncertainty in economics and that the Bayesian framework is the main acceptable for constructing that idea. The primary and unifying subject of this publication is determination making lower than uncertainty in microeconomic concept. Our basic target is to discover the ways that organisations and families make judgements and to increase versions that experience a robust empirical connection. hence, we now have tried to give a contribution to fiscal conception via formalizing versions of the particular professional cess of determination making below uncertainty. Bayesian method professional vides definitely the right motor vehicle for this formalization.
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Extra info for Bayesian Analysis and Uncertainty in Economic Theory
Test procedures based on this type of prior distribution require careful study, because they can exhibit some unusual features. Sequential Decision Problems In many statistical decision problems, the OM can obtain the observations ••• in a random sample one at a time. After each observation X" the OM can calculate the posterior distribution for e based on the observed values of XI, . . , X" and can decide whether to terminate the sampling process and choose a decision from D or to continue the sampling process and observe X,,+ I' A problem of this type is called a sequential decision problem.
At this stage, the total future risk from taking another observation and then making an optimal decision as to whether the final observation should be taken is c + E[PI(f)]. The risk from stopping without any further observations is again Po(~). Hence, if pi~) denotes the optimal total future risk when at most two observations remain to be taken, then (19) In general, if PII(~) denotes the optimal total future risk when at most 2. Bayesian Decision Theory n observations remain to be taken and the distribution of 25 e is i;, then (20) The relation (20) is known as the optimality equation or the dynamic programming equation.
In fact, every test of competing hypotheses is, at least theoretically, a problem with exactly two decisions: accept the null hypothesis H o, which we shall call decision do, and accept the alternative hypothesis HI (or, equivalently, reject H o), which we shall call decision d ,. Loss functions appropriate to testing hypotheses can easily be developed. For example, suppose that 8 is a real-valued parameter and it is desired to test the hypotheses Ho : 8 :::; aoand HI: 8 > ao, where aois a specified number.