Decision theory

H, Ohemoff and L. E. Moses, Elementary Decision Theory, John Wiley and Sons, Inc., New York, 1959 H. Cramer, Mathematical Method of Statistics, Princeton University Press, 1954. 

Decision Theory Formalism in the Behavioral Sciences.46—A formal method for examining decisions is developed through the use of a utility matrix [ tj] similar to the payoff matrix of game theory. In this matrix the rows correspond to the various possible acts of a decision-maker (e.g., to invest money in enterprises AltA2, -, Am) and the columns to various states, i.e., circumstances (e.g., possible levels of development of each enterprise) under which the acts are performed. The element y gives the utility (return or value) for using act At when state sf prevails. 

The following illustration of a decision process recently given by Gale and Shapley does not utilize the foregoing ideas on decision theory, but is both amusing and interesting in itself.47... 

In a tiny fraction of cases, a quick formula can be used. For most cases, the analysis uses an options tree, with one leaf per possible outcome. However, this falls prey to the curse of dimensionality —the number of leaves on the tree grows exponentially in the number of risk and decision dimensions considered. Thus only a limited, simple set of situations can be optimized in this way because one has to severely limit the decisions and risks that are considered. Tools available to help automate and simplify options analysis, widely used in pharmaceutical project evaluation, include Excel addons such as R1SK [11] and more graphically based solutions such as DPL [12]. Both of these support the creation and evaluation of decision trees and of influence diagrams Figure 11.2 shows a simple example of each of these. A primer in applied decision theory is Clemen s book Making Hard Decisions, other sources may be found in the website of James Vornov, Director of Clinical Research at Guildford Pharmaceuticals, a recent convert to decision theory for options analysis [13]. 

Therefore we increasingly take the view that rather than fully simulating the business context, which may seem like a black box approach, it is better to have decision makers interact with more selective simulations. These help develop their intuitions and hone their judgment and reasoning ability in focused areas, especially in the area of probability, applied statistics, and decision theory, which is nonintuitive without such practice. 

The decision theory is valid for variable costs but does not consider the problem of capacity allocation. In many contexts, screening capacity is a sunk cost, and there is a need to consider the straw that broke the camel s back, the first compound that exceeds capacity. There is no need to ration resources that are not scarce and have trivial variable costs relative to the potential value that their use can create. This reasoning leads naturally back to use of easily understood, intuitive flow and capacity visualizations for the relevant simulations. 

From both a theoretical and practical view, it is ideal to use Bayesian Decision Theory because it represents an optimal classifier. From a theoretical perspective, Bayesian Decision Theory offers a general definition of the pattern recognition problem and, with appropriate assumptions, it can be shown to be the basis of many of the so-called non-PDF approaches. In practice, however, it is typically treated as a separate method because it places strong data availability requirements for direct use compared to other approaches. 

From the decision variants and probabilities given above, the prediction values as applied in Eq. (4.53b) play an important role in decision theory, namely ... 

The National Academy of Sciences of Ukraine suggested that an economic-environmental-social model be devised and employed for the purposes of the country s sustainable development. This is a very complex and time-consuming approach that may not be usable at this time of industrial restructuring, privatization and other involved processes occurring in a collapsed national economy. An alternative tactics is put forward, which is applicable at both national and regional level. Instead of mathematical modeling and optimization, it uses systems approach and decision theory techniques. 

One-phase optimization Maximize expected profit across one or multiple price scenarios. This approach corresponds to the classical expect value maximization known from decision theory. 

The topic of eliciting probability distributions that are based purely on judgment (professional or otherwise) is discussed in texts on risk assessment (e.g., Moore 1983 Vose 2000) and decision theory or Bayesian methodology (e.g., Berger 1985). Elicitation methods may be considered with ID models in case no data are available for htting a model. In the 2D situation, elicitation may be used for the parameter uncertainty distribntions. In that situation, it may happen that no kind of relative fre-qnency data wonld be relevant, simply because the distributions represent subjective uncertainty and not relative frequency. 

Berger JO. 1985. Statistical decision theory and Bayesian analysis. New York Springer. 

Claxton K., L. GinneUy, M. Sculpher, Z. Philips, and S. Palmer. 2004. A Pilot Study on the Use of Decision Theory and Value of Information Analysis as Past of the National Health Service Technology Assessment Programme. Health Technology Assessment 8(31) (whole issue). 

J.O. Berger, Statistical Decision Theory and Bayesian Analysis, 2nd edn. (Springer-Verlag, New York, 1985)... 

Abelson RP, Levi A. 1985. Decision making and decision theory. In Handbook of Social Psychology, p. 231. New York Random House. 

ELEMENTARY DECISION THEORY, Herman Chemoff and Lincoln E. Moses. Clear introduction to statistics and statistical theory covers data processing, probability and random variables, testing hypotheses, much more. Exercises. 364pp. 5X x 8H. 65218-1 Pa. 38.95... 

Raiffa, H. A. and Schlaifer, R. S. (1961). Applied Statistical Decision Theory. MIT Press, Cambridge. 

Firmer, H. and Strassburger, K. (2002). The partitioning principle A powerful tool in multiple decision theory. Annals of Statistics, 30, 1194—1213. 

Fritsch, K. and Hsu, J. C. (1997). On analysis of means. In Advances in Statistical Decision Theory and Methodology. Editors N. Balakrishnan and S. Panchapakesan. Birkhauser, Boston, 114-119. 

Stefansson, G., Kim, W., and Hsu, J. C. (1988). On confidence sets in multiple comparisons. In Statistical Decision Theory and Related Topics IV, volume 2. Editors S. S. Gupta and J. O. Berger, pages 89-104. Springer-Verlag, New York. 

If risks are classified as tolerable, or if there is dispute as to whether they are tolerable or acceptable, risk management needs to design and implement actions that make these risks acceptable over time. Should this not be feasible then risk management, assisted by communication, needs at least to credibly convey the message that major effort is undertaken to bring these risks closer to being acceptable. This task can be described in terms of classic decision theory (Morgan 1990 Hammond et al. 1999). 

The recognition accuracy estimation described above faces one very important problem what is the best choice for the threshold value 0 To solve this problem, statistical decision theory is used. ° The basis for this is an analysis of the so-called the Received Operating Characteristic (ROC) curve. By tradition, ROC is plotted as a function of true positive rate TPj TP + FN) (or sensitivity) versus false positive rate FPj TN+FP) (or 1-Specificity) for all possible threshold values 0. Figure 6.5 presents an example of such a ROC curve for the results obtained with our computer program PASS in predicting antineoplastic activity. 

To obtain the qualitative ( Yes/No ) results of prediction, it is necessary to define the threshold Bk values for each kind of activity Ak- On the basis of statistical decision theory (Section 6.3.4) it is possible using the risk functions minimization, but nobody can a priori determine such functions for all kinds of activity and for all possible real-world problems. Therefore the predicted activity spectrum is presented in PASS by the list of activities with probabilities to be active Pa and to be inactive Pi calculated for each activity. The list is arranged in descending order of Pa—Pi, thus, the more probable activities are at the top of the list. The list can be shortened at any desirable cutoff value, but Pa>Pi is used by default. If the user chooses a rather high value of Pa as a cutoff for selection of probable activities, the chance to confirm the predicted activities by the experiment is high too, but many activities will be lost. For instance, if Pq>80% is used as a threshold, about 80% of real activities will be lost for Pq>70%, the portion of lost activities is 70%, etc. 

Condensation of information is obtained through formal calculations of central values and dispersions without prejudice as to the type of distribution. Interpretation of the meaning of the information obtained is another matter. Here knowledge of statistical decision theory is helpful.Statistical tools should be employed as aids to common sense. 

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