Ward Edwards

Bayesian Statistical Inference for Psychological Research

Bayesian statistics, a currently controversial viewpoint concerning statistical inference, is based on a definition of probability as a particular measure of the opinions of ideally consistent people. Statistical inference is modification of these opinions in the light of evidence, and Bayes’ theorem specifies how such modifications should be made. The tools of Bayesian statistics include the theory of specific distributions and the principle of stable estimation, which specifies when actual prior opinions may be satisfactorily approximated by a uniform distribution. A common feature of many classical significance tests is that a sharp null hypothesis is compared with a diffuse alternative hypothesis. Often evidence which, for a Bayesian statistician, strikingly supports the null hypothesis leads to rejection of that hypothesis by standard classical procedures. The likelihood principle emphasized in Bayesian statistics implies, among other things, that the rules governing when data collection stops are irrelevant to data interpretation. It is entirely appropriate to collect data until a point has been proven or disproven, or until the data collector runs out of time, money, or patience.

How to Use Multiattribute Utility Measurement for Social Decisionmaking

Arguments over public policy typically turn out to hinge on disagreements about public values. Often, those in conflict may agree about what the relevant dimensions of value are. The conflicts arise over the relative importance of various goals. Normally, such disagreements are fought out in the contexts of specific decisions, and so are fought out over and over again, at enormous social cost each time another decision must be made. This paper proposes a method that can spell out explicitly what each individuals or groups values are, showing how and how much they differ-and in the process can frequently reduce the extent of such differences. It presents data illustrating the application of this technology, multiattribute utility measurement, to two specific instances: management of the coastal zone of the town of Venice, a part of Los Angeles, CA; and selection of research programs for the Office of Child Development, Department of Health, Education, and Welfare. In both cases, exploitation of multiattribute utility measurement permits the decisionmaking or regulatory agencies to shift their attention from the specific actions, being regulated to the values these actions serve and the decisionmaking mechanisms that implement these values. In the process, the data show that degree of disagreement about values among holders of conflicting value systems are often reduced.

Dynamic Decision Theory and Probabilistic Information Processings

The development of a dynamic decision theory will be central to the impending rapid expansion of research on human decision processes. Of a taxonomy of six decision problems, five require a dynamic theory in which the decision maker is assumed to make a sequence of decisions, basing decision n + 1 on what he learned from decision n and its consequences. Kesearch in progress on information seeking, intuitive statistics, sequential prediction, and Bayesian information processing is reviewed to illustrate the kind of work needed. The relevance of mathematical developments in dynamic programming and Bayesian statistics to dynamic decision theory is examined. A man-computer system for probabilistic processing of fallible military information is discussed in some detail as an application of these ideas and as a setting and motivator for future research on human information processing and decision making.

Optimal strategies for seeking information: Models for statistics, choice reaction times, and human information processing.

Abstract Models for optional stopping in statistics are also normative models for tasks in which subjects may purchase risk-reducing information before making a decision. A Bayesian model for optional stopping for the two-hypothesis continuous case is developed; it takes explicit account of cost of information, values of the possible outcomes of the final decision, and prior probabilities of the hypotheses. A nonparametric model for choice reaction times is derived. It makes strong predictions about times and errors; only one quantity in it is not directly observable. A second example uses the model to design and predict results of a binomial information-purchase experiment.

A comparison of weight approximation techniques in multiattribute utility decision making

Abstract The notion of “dominance” in multiattribute utility decision contexts leads to a change in the considered alternative set. The implications of this set change are discussed in relation to the conditions of Wainers (1976) “equal-weights theorem,” and the possibility of sensitivity to weighting of importance dimensions is demonstrated. Data from three multiattribute decision-making studies are examined using four rank weighting techniques as well as equal weights in order to examine the practical significance of this sensitivity. Correlations between measures of overall utility produced by each weighting technique suggest that rank weighting of dimensions results in some improvement over equal weighting. This improvement was not always, however, reflected by significant changes in decisions.

Advances in decision analysis : from foundations to applications

Ch 3: The Foundations of Decision Analysis Revisited Citation: Howard RA. Chapter 3: The Foundations of Decision Analysis Revisited. Edwards W, Miles RF, von Winterfeldt D, eds. Advances in Decision Analysis: From Foundations to Applications. Cambridge University Press 2007: 32-56. http://www.cambridge.org/9780521863681 Ch 4: Decision Analysis: A Personal Account of How It Got Started and Evolved Citation: Raiffa H. Chapter 4: Decision Analysis: A Personal Account of How It Got Started and Evolved. Edwards W, Miles RF, von Winterfeldt D, eds. Advances in Decision Analysis: From Foundations to Applications. Cambridge University Press 2007: 57-70. http://www.cambridge.org/9780521863681

Hailfinder: A Bayesian system for forecasting severe weather

Abstract Hailfinder is a Bayesian system that combines meteorological data and model with expert judgment, based on both experience and physical understanding, to forecast severe weather in Northeastern Colorado. The system is based on a model, known as a belief network (BN), that has recently emerged as the basis of some powerful intelligent systems. Hailfinder is the first such system to apply these Bayesian models in the realm of meteorology, a field that has served as the basis of many past investigations of probabilistic forecasting. The design of Hailfinder provides a variety of insights to designers of other BN-based systems, regardless of their fields of application.

Eliciting Subjective Probability Distributions on Continuous Variables

Abstract Five procedures for assessing subjective probability distributions over continuous variables were compared using almanac questions as stimuli. The procedures varied on the uncertainty measures used (probabilities, odds, and odds on a logarithmic scale) and the type of response required from the subjects (uncertainty measure or value of the unknown quantity). The results showed the often used fractile procedures were inferior to procedures requiring probabilities or odds as the response from subjects. The results are also discussed in terms of the “anchoring and adjustment” hypothesis.

Costs and payoffs in perceptual research.

Abstract : A persistent problem in psychological research that reaches conclusions about inaccessible processes or experiences inside a subjects head is to validate those conclusions--that is, to exhibit persuasive reasons to believe that emitted behavior in some sense faithfully reports inaccessible processes. In the mid-1950s, perceptual researchers widely adopted an approach that might be called validation by cupidity. If the experimenter is willing to define a correct response, he can reward the subject for correct responses and not for wrong ones; however, costs and payoffs are rather feeble means of instructing a subject what to do, or of ensuring that he does it.

Personal probabilities of probabilities

By definition, the subjective probability distribution of a random event is revealed by the (‘rational’) subjects choice between bets — a view expressed by F. Ramsey, B. De Finetti, L. J. Savage and traceable to E. Borel and, it can be argued, to T. Bayes. Since hypotheses are not observable events, no bet can be made, and paid off, on a hypothesis. The subjective probability distribution of hypotheses (or of a parameter, as in the current ‘Bayesian’ statistical literature) is therefore a figure of speech, an ‘as if’, justifiable in the limit. Given a long sequence of previous observations, the subjective posterior probabilities of events still to be observed are derived by using a mathematical expression that would approximate the subjective probability distribution of hypotheses, if these could be bet on. This position was taken by most, but not all, respondents to a ‘Round Robin’ initiated by J. Marschak after M. H. De-Groots talk on Stopping Rules presented at the UCLA Interdisciplinary Colloquium on Mathematics in Behavioral Sciences. Other participants: K. Borch, H. Chernoif, R. Dorfman, W. Edwards, T. S. Ferguson, G. Graves, K. Miyasawa, P. Randolph, L. J. Savage, R. Schlaifer, R. L. Winkler. Attention is also drawn to K. Borchs article in this issue.