Bayesian Analysis - A Method for Updating Risk Estimates

Abstract

In the first stages of formulating decision strategies, risk estimates may have to be based on sketchy information and limited experience. It is often important to be able to revise, or improve, the original risk estimates as new information becomes available. This is where Bayesian analysis comes in. Introduction In recent years there has been a great deal of emphasis on the use of expected-value concepts in the analysis of decisions under uncertainty. Expected values are risk-adjusted criteria that can be used by the decision maker to compare and select capital investment projects. A significant aspect of expected value criteria is that they provide a means to express the degree of risk and uncertainty in quantitative terms. These quantitative risk statements (or estimates) are the probabilities of occurrence of the various possible outcomes of a decision choice. As one might suspect, the probability numbers, or risk estimates, are critical factors in the expected value analysis of decisions involving risk and uncertainty. Frequently we must analyze decision choices in situations where there is very little information or experience upon which to base the risk estimates. Although these probabilities may be only approximate, they presumably represent the best estimates of risk at the time of presumably represent the best estimates of risk at the time of decision making and must be used to formulate initial decision strategies. It is often important to be able to revise, or improve, the original risk estimates as new information becomes available. This is where Bayesian analysis comes in. The purpose of this paper is to explain the logic and philosophy of Bayesian analysis - a formalized, statistical method philosophy of Bayesian analysis - a formalized, statistical method of updating risk analysis. First we shall consider Bayes' theorem and the mechanics of Bayesian computations. Then we shall discuss how Bayesian analysis is used in situations involving a series of new information - that is, in sequential sampling. Finally, we shall discuss the key issues of both sides of the controversy that surrounds the use of Bayesian analysis in business decisions. The Decision-Making Process - An Overview The decision-making process is actually a series of steps, or phases. Enumeration of these steps makes clearer the role of phases. Enumeration of these steps makes clearer the role of Bayesian analysis:Define the possible outcomes (states of nature) and the decision choices available to the decision maker.Associate the probabilities of occurrence and economic considerations with each of the possible outcomes.Select investment strategy, based on expected-value criteria.Note the results (outcomes) of the initial choice.Revise the risk estimates using Bayesian analysis and whatever information stems from Step 4.Modify the investment strategy, if necessary, on the basis of new expected-value analysis and revised risk estimates. The first three steps are basic to the initial quantitative analysis of any investment decision involving uncertainty. The remaining steps represent a "monitoring system" to provide the basis for managerial decisions regarding changes in investment strategies with time. JPT P. 193

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