Scholars@Duke
Robert L. Winkler

Robert L. Winkler

James B. Duke Distinguished Professor Emeritus of Business Administration
Fuqua School of Business
rwinkler@duke.edu
Box 90120, Durham, NC 27708-0120
Fuqua Sch of Bus, Durham, NC 27708

Selected Publications

Multivariate Almost Stochastic Dominance: Transfer Characterizations and Sufficient Conditions Under Dependence Uncertainty

Journal Article Operations Research · March 1, 2025 Most often, important decisions involve several unknown attributes. This produces a double challenge in the sense that both assessing the individual multiattribute preferences and assessing the joint distribution of the attributes can be extremely hard. To ... Full text Cite

RESOLUTE AND CORRELATED BAYESIANS

Journal Article Philosophers Imprint · January 1, 2025 This paper suggests a new normative approach for combining beliefs. We call it the evidence-first method. Instead of aggregating credences alone, as the prevailing approaches, we focus instead on eliciting a group’s full probability distribution on the bas ... Full text Cite

Normativity, Epistemic Rationality, and Noisy Statistical Evidence

Journal Article British Journal for the Philosophy of Science · March 1, 2024 Many philosophers have argued that statistical evidence regarding group characteristics (particularly stereotypical ones) can create normative conflicts between the requirements of epistemic rationality and our moral obligations to each other. In a recent ... Full text Cite

The M5 uncertainty competition: Results, findings and conclusions

Journal Article International Journal of Forecasting · October 1, 2022 This paper describes the M5 “Uncertainty” competition, the second of two parallel challenges of the latest M competition, aiming to advance the theory and practice of forecasting. The particular objective of the M5 “Uncertainty” competition was to accurate ... Full text Cite

Evaluating quantile forecasts in the M5 uncertainty competition

Journal Article International Journal of Forecasting · October 1, 2022 Probabilistic forecasts are necessary for robust decisions in the face of uncertainty. The M5 Uncertainty competition required participating teams to forecast nine quantiles for unit sales of various products at various aggregation levels and for different ... Full text Cite

Extremizing and Antiextremizing in Bayesian Ensembles of Binary-Event Forecasts

Journal Article Operations Research · September 1, 2022 Probability forecasts of binary events are often gathered from multiple models or experts and averaged to provide inputs regarding uncertainty in important decision-making problems. Averages of well-calibrated probabilities are underconfident, and methods ... Full text Cite

Technical Note—Ranking Distributions When Only Means and Variances Are Known

Journal Article Operations Research · September 1, 2022 Consider a choice between two random variables, for which only means and variances are known. Is it possible to rank them by putting some constraints on risk preferences? We provide such a ranking by bounding how much marginal utility can change. Such boun ... Full text Cite

Forecasting: theory and practice

Journal Article International Journal of Forecasting · July 1, 2022 Forecasting has always been at the forefront of decision making and planning. The uncertainty that surrounds the future is both exciting and challenging, with individuals and organisations seeking to minimise risks and maximise utilities. The large number ... Full text Cite

Why do some combinations perform better than others?

Journal Article International Journal of Forecasting · January 1, 2020 The evidence from the literature on forecast combination shows that combinations generally perform well. We discuss here how the accuracy and diversity of the methods being combined and the robustness of the combination rule can influence performance, and ... Full text Cite

Probabilistic tornado forecasts: some experimental results.

Journal Article · January 1, 2020 Some preliminary results of an experiment in which NWS forecasters at the National Severe Storms Forecast Center (NSSFC) expressed forecasts of tornado occurrence and intensity in probabilistic terms are described. (from paper) (REF CONTD)(Omaha, Nebraska, ... Cite

Probability forecasts and their combination: A research perspective

Journal Article Decision Analysis · January 1, 2019 We explore some recent, and not so recent, developments concerning the use of probability forecasts and their combination in decision making. Despite these advances, challenges still exist. We expand on some important challenges influencing the “goodness” ... Full text Cite

Multivariate Almost Stochastic Dominance

Journal Article Journal of Risk and Insurance · June 1, 2018 Almost stochastic dominance allows small violations of stochastic dominance rules to avoid situations where most decision makers prefer one alternative to another but stochastic dominance cannot rank them. We present the concepts of multivariate almost sto ... Full text Cite

When to abandon a research project and search for a new one

Journal Article Operations Research · May 1, 2018 We investigate the cost of the opportunity delayed by working on one project with uncertain success rather than searching for a new project. We answer this question: How long should a firm work on a research project with uncertain success before abandoning ... Full text Cite

Between first- and second-order stochastic dominance

Journal Article Management Science · September 1, 2017 We develop a continuum of stochastic dominance rules, covering preferences from first- to second-order stochastic dominance. The motivation for such a continuum is that while decisionmakers have a preference for "more is better," they aremostly risk averse ... Full text Cite

Quantile evaluation, sensitivity to bracketing, and sharing business payoffs

Journal Article Operations Research · May 1, 2017 From forecasting competitions to conditional value-at-risk requirements, the use of multiple quantile assessments is growing in practice. To evaluate them, we use a rule from the general class of proper scoring rules for a forecaster's multiple quantiles o ... Full text Cite

Combining interval forecasts

Journal Article Decision Analysis · March 1, 2017 When combining forecasts, a simple average of the forecasts performs well, often better than more sophisticated methods. In a prescriptive spirit, we consider some other parsimonious, easy-to-use heuristics for combining interval forecasts and compare thei ... Full text Cite

Probabilistic tornado forecasts: some experimental results.

Journal Article · January 1, 2017 Some preliminary results of an experiment in which NWS forecasters at the National Severe Storms Forecast Center (NSSFC) expressed forecasts of tornado occurrence and intensity in probabilistic terms are described. (from paper) (REF CONTD)(Omaha, Nebraska, ... Cite

Generalized almost stochastic dominance

Journal Article Operations Research · March 1, 2015 Almost stochastic dominance allows small violations of stochastic dominance rules to avoid situations where most decision makers prefer one alternative to another but stochastic dominance cannot rank them. While the idea behind almost stochastic dominance ... Full text Cite

The importance of communicating uncertainties in forecasts: overestimating the risks from winter storm Juno.

Journal Article Risk analysis : an official publication of the Society for Risk Analysis · March 2015 Full text Cite

Equal versus differential weighting in combining forecasts.

Journal Article Risk analysis : an official publication of the Society for Risk Analysis · January 2015 Full text Cite

Is it better to average probabilities or quantiles?

Journal Article Management Science · January 1, 2013 We consider two ways to aggregate expert opinions using simple averages: averaging probabilities and averaging quantiles. We examine analytical properties of these forecasts and compare their ability to harness the wisdom of the crowd. In terms of location ... Full text Cite

Log-Optimal Economic Evaluation of Probability Forecasts

Journal Article Journal of the Royal Statistical Society Series A: Statistics in Society · July 1, 2012 SummaryThe commercial test of an expert’s probability assessments is not that they are accurate in an abstract sense, but that they yield financial returns to decision makers. From this utilitarian standpoint, a model or fo ... Full text Cite

Multiattribute one-switch utility

Journal Article Management Science · March 1, 2012 The one-switch property states that the preference between any two lotteries switches at most once as wealth increases. Working within the expected utility framework, we extend the one-switch notion to the multiattribute case and identify the families of m ... Full text Cite

On multivariate quantiles under partial orders

Journal Article The Annals of Statistics · April 1, 2011 Full text Cite

Tailored scoring rules for probabilities

Journal Article Decision Analysis · January 1, 2011 When scoring rules were first widely used, they were developed as a way to measure the accuracy of probability forecasts ex post. Ex ante, proper scoring rules encourage honestly reported and sharper probabilities, both of which increase the forecaster's e ... Full text Cite

Multivariate Concave and Convex Stochastic Dominance

Scholarly Edition · April 23, 2010 Cite

Scoring Rules

Chapter · January 1, 2010 Probabilities are used to quantify uncertainty in operations research and management science modeling. Scoring rules provide a numerical measure (a score or reward) based on probabilities for an event or variable and on what actually occurs. As such, they ... Full text Cite

Multiattribute utility satisfying a preference for combining good with bad

Journal Article Management Science · December 1, 2009 An important challenge in multiattribute decision analysis is the choice of an appropriate functional form for the utility function. We show that if a decision maker prefers more of any attribute to less and prefers to combine good lotteries with bad, as o ... Full text Cite

Duality between maximization of expected utility and minimization of relative entropy when probabilities are imprecise

Conference Isipta 2009 Proceedings of the 6th International Symposium on Imprecise Probability Theories and Applications · December 1, 2009 In this paper we model the problem faced by a riskaverse decision maker with a precise subjective probability distribution who bets against a risk-neutral opponent or invests in a financial market where the beliefs of the opponent or the representative age ... Cite

Evaluating quantile assessments

Journal Article Operations Research · September 1, 2009 Quantile assessments are commonly encountered in the elicitation of probability distributions in decision analysis, forecasting, and risk analysis. Scoring rules have been developed to provide ex ante incentives for careful and truthful assessments and ex ... Full text Cite

Sensitivity to distance and baseline distributions in forecast evaluation

Journal Article Management Science · April 1, 2009 Scoring rules can provide incentives for truthful reporting of probabilities and evaluation measures for the probabilities after the events of interest are observed. Often the space of events is ordered and an evaluation relative to some baseline distribut ... Full text Cite

Scoring rules, generalized entropy, and utility maximization

Journal Article Operations Research · September 1, 2008 Information measures arise in many disciplines, including forecasting (where scoring rules are used to provide incentives for probability estimation), signal processing (where information gain is measured in physical units of relative entropy), decision an ... Full text Cite

Simple robust averages of forecasts: Some empirical results

Journal Article International Journal of Forecasting · January 1, 2008 An extensive body of literature has shown that combining forecasts can improve forecast accuracy, and that a simple average of the forecasts (the mean) often does better than more complex combining schemes. The fact that the mean is sensitive to extreme va ... Full text Cite

Scoring rules, entropy, and imprecise probabilities

Journal Article Isipta 2007 Proceedings of the 5th International Symposium on Imprecise Probability Theories and Applications · December 1, 2007 Suppose that a risk-averse expected utility maximizer with a precise probability distribution p bets opti- mally against a risk neutral opponent (or equiva- lently invests in an incomplete market for contingent claims) whose beliefs (or prices) are describ ... Cite

Probability elicitation, scoring rules, and competition among forecasters

Journal Article Management Science · November 1, 2007 Probability forecasters who are rewarded via a proper scoring rule may care not only about the score, but also about their performance relative to other forecasters. We model this type of preference and show that a competitive forecaster who wants to do be ... Full text Cite

Decision making with multiattribute performance targets: The impact of changes in performance and target distributions

Journal Article Operations Research · March 1, 2007 In many situations, performance on several attributes is important. Moreover, a decision maker's utility may depend not on the absolute level of performance on each attribute, but rather on whether that level of performance meets a target, in which case th ... Full text Cite

Aggregating probability distributions

Chapter · January 1, 2007 This chapter is concerned with the aggregation of probability distributions in decision and risk analysis. Experts often provide valuable information regarding important uncertainties in decision and risk analyses because of the limited availability of har ... Full text Cite

On Equivalent Target-Oriented Formulations for Multiattribute Utility

Journal Article Decision Analysis · June 2006 Targets are used quite often as a management tool, and it has been argued that thinking in terms of targets may be more natural than thinking in terms of utilities. The standard expected-utility framework with a single attribute (such as money) an ... Full text Cite

The optimizer's curse: Skepticism and postdecision surprise in decision analysis

Journal Article Management Science · March 1, 2006 Decision analysis produces measures of value such as expected net present values or expected utilities and ranks alternatives by these value estimates. Other optimization-based processes operate in a similar manner. With uncertainty and limited resources, ... Full text Cite

Risky choices and correlated background risk

Journal Article Management Science · September 1, 2005 The analysis of a risky project should take into account not only uncertainties about the return from, that project ("project risk"), but also uncertainties associated with other ongoing projects and with exogenous factors that can impact final wealth ("ba ... Full text Cite

On uncertainty in medical testing.

Journal Article Medical decision making : an international journal of the Society for Medical Decision Making · November 2004 There is confusion in the medical decision-making literature about how to handle uncertainty in medical tests. In this article, the authors consider the situation in which there is uncertainty about the pretest probability of a disease in a patient as well ... Full text Cite

Strategic choice of variability in multiround contests and contests with handicaps

Journal Article Journal of Risk and Uncertainty · September 1, 2004 Variability can be an important strategic variable in a contest. We study optimal strategies involving choice of variability in contests with fixed and probabilistic targets, one-round and multiround contests, contests with and without handicaps, and situa ... Full text Cite

Multiple Experts vs. Multiple Methods: Combining Correlation Assessments

Journal Article Decision Analysis · September 2004 Averaging forecasts from several experts has been shown to lead to improved forecasting accuracy and reduced risk of bad forecasts. Similarly, it is accepted knowledge in decision analysis that an expert can benefit from using more than one assess ... Full text Cite

Modifying variability and correlations in winner-take-all contests

Journal Article Operations Research · May 1, 2004 We consider contests with a fixed proportion of winners based on relative performance. Special attention is paid to winner-take-all contests, which we define as contests with relatively few winners receiving relatively large awards, but we consider the ful ... Full text Cite

An Introduction to Bayesian Inference and Decision

Book · January 1, 2003 CD-ROM contains: Beta Distribution Generator (Excel file) ; Binomial Distribution Generator (Excel file) ; book exercises (MS Word files) ; book figures (Powerpoint files) ; TreeAge Data decision trees for some of the examples in the book ; ... ... Cite

The role of informative priors in zero-numerator problems: Being conservative versus being candid

Journal Article American Statistician · January 1, 2002 The "Rule of Three" gives an approximation for an upper 95% confidence bound for a proportion in a zero-numerator problem, which occurs when the observed relative frequency is zero. We compare the results from the Rule of Three with those from a Bayesian a ... Full text Cite

Why Bayesian analysis hasn't caught on in healthcare decision making.

Journal Article International journal of technology assessment in health care · January 2001 The objective of this paper is to discuss why Bayesian statistics is not used more in healthcare decision making and what might be done to increase the use of Bayesian methods. First, a case is made for why Bayesian analysis should be used more widely. Ser ... Full text Cite

The first positive: computing positive predictive value at the extremes.

Journal Article Annals of internal medicine · May 2000 Computing the positive predictive value (PPV) of a wellknown test for a relatively common disease is a straight-forward exercise. However, in the case of a new test for a rare disorder; the extreme numbers involved-the very low prevalence of the disorder a ... Full text Cite

Assessing dependence: some experimental results

Journal Article Management Science · January 1, 2000 Constructing decision- and risk-analysis probability models often requires measures of dependence among variables. Although data are sometimes available to estimate such measures, in many applications they must be obtained by means of subjective judgment b ... Full text Cite

Combining probability distributions from experts in risk analysis

Journal Article Risk Analysis · April 1, 1999 This paper concerns the combination of experts' probability distributions in risk analysis, discussing a variety of combination methods and attempting to highlight the important conceptual and practical issues to be considered in designing a combination pr ... Full text Cite

Casey's problem: Interpreting and evaluating a new test

Journal Article Interfaces · January 1, 1999 Casey, the newborn daughter of one of the authors of this paper, received a positive result on an experimental medical screening test, indicating that she may lack an enzyme required to digest certain fats. The interpretation of this test result was compli ... Full text Cite

Evaluation of probabilities: A level playing field?

Conference DECISION SCIENCE AND TECHNOLOGY: REFLECTIONS ON THE CONTRIBUTIONS OF WARD EDWARDS · January 1, 1999 Link to item Cite

Combining Patient Utility with Health Status Assessment to Improve Medical Decision Making

Journal Article Journal of Multi‐Criteria Decision Analysis · December 1996 Full text Cite

Uncertainty in probabilistic risk assessment

Journal Article Reliability Engineering and System Safety · November 1, 1996 Dealing with uncertainty is an important and difficult aspect of analyses for complex systems. Such systems involve many uncertainties, and assessing probabilities to represent these uncertainties is itself a complex undertaking utilizing a variety of info ... Full text Cite

Combining patient utility with health status assessment to improve medical decision making

Journal Article Journal of Multi Criteria Decision Analysis · January 1, 1996 Physicians often use health status assessment tools to evaluate a patient’s condition, then apply established guidelines to determine the most medically effective treatment. Yet additional criteria, such as the appropriateness of the treatment given the pa ... Full text Cite

Scoring rules and the evaluation of probabilities

Journal Article Test · January 1, 1996 In Bayesian inference and decision analysis, inferences and predictions are inherently probabilistic in nature. Scoring rules, which involve the computation of a score based on probability forecasts and what actually occurs, can be used to evaluate probabi ... Full text Cite

Hailfinder: A Bayesian system for forecasting severe weather

Journal Article International Journal of Forecasting · January 1, 1996 Hailfinder is a Bayesian system that combines meteorological data and models 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 n ... Full text Cite

Coherent combination of experts' opinions

Journal Article Test · December 1, 1995 An expert (for You) is here defined as someone who shares Your world-view, but knows more than You do, so that were She to reveal Her current opinion to You, You would adopt it as Your own. When You have access to different experts, with differing informat ... Full text Cite

Screening probability forecasts: contrasts between choosing and combining

Journal Article International Journal of Forecasting · January 1, 1995 In many forecasting situations, forecasts can be produced by several different methods. The ultimate objective of considering multiple methods may be to select a single method (the choosing scenario) or to aggregate the multiple forecasts into a single for ... Full text Cite

Assessment of the risk of chronic lung injury attributable to long-term ozone exposure

Journal Article Operations Research · January 1, 1995 This paper presents an application of a formal process for encoding experts' probabilistic judgments. The objective is to characterize scientific judgment regarding the risk of chronic lung injury to children aged 8 through 16 and to adult outdoor workers ... Full text Cite

The impact of testing errors on value of information: A quality-control example

Journal Article Journal of Risk and Uncertainty · January 1, 1995 In this article, we extend recent work on the inferential impact of errors in data to a decision-making setting. In the context of a simple quality-control example, we illustrate how errors can cause substantial reductions in the value of information from ... Full text Cite

Evaluating Probabilities: Asymmetric Scoring Rules

Journal Article Management Science · November 1994 Proper scoring rules are over evaluation measures that reward accurate probabilities Specific rules encountered in the literature and used in practice are invariably symmetric in the sense that the expected score for a perfectly-calibrated probabi ... Full text Cite

VALUED-FOCUSED THINKING

Journal Article SLOAN MANAGEMENT REVIEW · September 1, 1994 Link to item Cite

Several Bayesians: A review

Journal Article Test · December 1, 1993 This paper synthesizes a number of papers in which the author has participated that all concern models in which several decision-makers, each modeled as a Bayesian, appear. The areas covered include amalgamation of opinion, treating expert opinion as data, ... Full text Cite

Aggregating point estimates. A flexible modeling approach

Journal Article Management Science · January 1, 1993 In many decision situations information is available from a number of different sources. Aggregating the diverse bits of information is an important aspect of the decision-making process but entails special statistical modeling problems in characterizing t ... Full text Cite

Evaluating and combining physicians' probabilities of survival in an intensive care unit

Journal Article Management Science · January 1, 1993 In this paper, probabilities of survival assessed by physicians for patients admitted to an intensive care unit are studied. The probabilities from each of four types of physicians are evaluated on an overall basis and in terms of specific attributes, and ... Full text Cite

Ambiguity and decision modeling: A preference-based approach

Journal Article Journal of Risk and Uncertainty · October 1, 1992 In this article, we develop a model that permits a decision maker's preferences to depend on the decision maker's ambiguity about the probability of an event that is relevant for decision-making purposes. We deal with ambiguity through preference modeling, ... Full text Cite

Implications of Errors in Survey Data: A Bayesian Model

Journal Article Management Science · July 1992 Data from surveys often include errors, and such errors can have a serious effect on inferences about behavior or perceptions. In this paper a model is developed for making inferences based on dichotomous survey data with possible errors. A likeli ... Full text Cite

Repeated Gambles, Learning, and Risk Aversion

Journal Article Management Science · June 1992 We analyze a decision problem with repeated gambles and find that under some seemingly reasonable risk-averse utility functions, recommended behavior for the initial decision can be highly risk-taking and counterintuitive. Further analysis reveals ... Full text Cite

Sensitivity of Weights in Combining Forecasts

Journal Article Operations Research · June 1992 In the combination of forecasts, weighted averages that attempt to take into account the accuracy of the forecasts and any dependence among forecasts tend to perform poorly in practice. An important factor influencing this performance is the sensi ... Full text Cite

The effect of nonstationarity on combined forecasts

Journal Article International Journal of Forecasting · January 1, 1992 Previous research on the combination of forecasts has, for the most part, implicitly assumed a stationary underlying process so that parameters could be estimated from historical data. While some models weight recent data more heavily in the estimation pro ... Full text Cite

On seeking a best performance measure or a best forecasting method

Journal Article International Journal of Forecasting · January 1, 1992 Full text Cite

Diagnostic verification of probability forecasts

Journal Article International Journal of Forecasting · January 1, 1992 Verification of probability forecasts traditionally consists largely of the computation of a few overall performance measures. This paper outlines a diagnostic approach to the evaluation of probability forecasts. The basic elements of this approach are the ... Full text Cite

Ambiguity, probability, preference, and decision analysis

Journal Article Journal of Risk and Uncertainty · July 1, 1991 The possible influence of ambiguity on decisions about probabilities has received considerable attention, with most modeling efforts focusing on the probabilities. In this article, it is argued that effects of ambiguity on decision making often operate via ... Full text Cite

DATA-BASE ERROR TRAPPING AND PREDICTION

Journal Article JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION · 1991 Full text Cite

Are two (inexperienced) heads better than one (experienced) head? Averaging house officers' prognostic judgments for critically ill patients.

Journal Article Archives of internal medicine · September 1990 Inexperienced physicians may make prognostic judgments and management decisions about acutely ill patients in the absence of supervision. We hypothesized that mathematically combining judgments of junior and senior house officers might yield aggregate judg ... Full text Cite

Unanimity and Compromise Among Probability Forecasters

Journal Article Management Science · July 1990 When two forecasters agree regarding the probability of an uncertain event, should a decision maker adopt that probability as his or her own? A decision maker who does so is said to act in accord with the unanimity principle. We examine a variety ... Full text Cite

Decision Modeling and Rational Choice: AHP and Utility Theory

Journal Article Management Science · March 1990 Full text Cite

Murder and (of?) the likelihood principle: A Trialogue

Journal Article Journal of Behavioral Decision Making · January 1, 1990 The Likelihood Principle of Bayesian inference asserts that only likelihoods matter to single‐stage inference. A likelihood is the probability of evidence given a hypothesis multiplied by a positive constant. The constant cancels out of simple versions of ... Full text Cite

Representing and Communicating Uncertainty

Journal Article Statistical Science · 1990 Cite

Comment: Representing and communicating uncertainty

Journal Article Statistical Science · January 1, 1990 Full text Cite

A health risk assessment for use in setting the U.S. primary ozone standard

Journal Article Studies in Environmental Science · December 1, 1989 This paper describes the results of a U.S. assessment of the ozone-Induced acute pulmonary health risks associated with attainment of three alternative 1-hour average ozone standards: 0.12 ppm (current U.S. standard), 0.10 ppm, and 0.08 ppm. Risk results a ... Full text Cite

Combining forecasts: A philosophical basis and some current issues

Journal Article International Journal of Forecasting · January 1, 1989 A philosophical basis for combining forecasts and some important current issues in the area of combining forecasts are discussed briefly. The philosophical basis views forecasts as information and the combination of forecasts in terms of aggregation of inf ... Full text Cite

SAMPLING DISTRIBUTIONS OF POST-SAMPLE FORECASTING ERRORS

Journal Article JOURNAL OF THE ROYAL STATISTICAL SOCIETY SERIES C-APPLIED STATISTICS · January 1, 1989 Link to item Cite

Uncertainty about processes that shift over time: Modeling and analysis

Journal Article Journal of Business and Economic Statistics · January 1, 1989 Full text Cite

All Roads Lead to Risk Preference: A Turnpike Theorem for Conditionally Independent Returns

Journal Article Journal of Financial and Quantitative Analysis · January 1, 1989 An individual is repeatedly offered the opportunity to invest in a risky asset whose return distribution is unknown. Because the return distribution is constant over time, however, he is able to learn about that distribution by observing investment outcome ... Full text Cite

Separating probability elicitation from utilities

Journal Article Journal of the American Statistical Association · January 1, 1988 This article deals with the separation of probability elicitation from utilities. We show that elicited probabilities can be related to utilities not just through the explicit or implicit payoffs related to the elicitation process, but also through other s ... Full text Cite

A general framework for forecast verification

Journal Article Monthly Weather Review · January 1, 1987 A general framework for forecast verification based on the joint distribution of forecasts and observations is described: 1) the calibration-refinement factorization, which involves the conditional distributions of observations given forecasts and the marg ... Full text Cite

Expert Resolution

Journal Article Management Science · March 1986 This paper discusses some current issues in the combination of probabilities and serves as an introduction to a series of four papers and a rejoinder relating to a paper by Morris (Morris, P. A. 1983. An axiomatic approach to expert resolution. Ma ... Full text Cite

Combining economic forecasts

Journal Article Journal of Business and Economic Statistics · January 1, 1986 A method for combining forecasts may or may not account for dependence and differing precision among forecasts. In this article we test a variety of such methods in the context of combining forecasts of GNP from four major econometric models. The methods i ... Full text Cite

Comment

Journal Article Statistical Science · January 1, 1986 Full text Cite

Market structure. The specialist as dealer and broker

Journal Article Journal of Banking and Finance · January 1, 1986 Models of a specialist's spread-setting behavior have focused on the specialist's role as a dealer and have generally not considered competition from limit orders. In this paper, a model of spread-setting behavior is described and used to study the competi ... Full text Cite

Combining Economic Forecasts

Journal Article Journal of Business & Economic Statistics · January 1986 Full text Cite

Dynamic Generalized Linear Models and Bayesian Forecasting: Comment

Journal Article Journal of the American Statistical Association · March 1985 Full text Cite

Comment: Bayesian model building and forecasting

Journal Article Journal of the American Statistical Association · January 1, 1985 Full text Cite

LIMITS FOR THE PRECISION AND VALUE OF INFORMATION FROM DEPENDENT SOURCES.

Journal Article Operations Research · January 1, 1985 The model given was based on information sources that provide estimates with a joint distribution of estimation errors. The case in which the joint distribution is multivariate normal received special attention because it is tractable and should often prov ... Full text Cite

EVALUATING DECISION STRATEGIES FOR EQUITY OF PUBLIC RISKS.

Journal Article Operations Research · January 1, 1985 This paper defines a concept of ex ante risk equity to address the equity of the process and distinguishes this concept from the ex post risk equity of the fatalities. The paper indicates that an analyis of decision strategies addresses ex ante equity. In ... Full text Cite

Research Needs and the Phenomena of Decisionmaking and Operations

Journal Article IEEE Transactions on Systems Man and Cybernetics · January 1, 1985 An April 1984 workshop on research directions was sponsored by the Decision and Management Science Program of the National Science Foundation at the University of Texas at Dallas. One session concerned the relationship of research to phenomena in decisionm ... Full text Cite

The use of probabilities in subjective quantitative precipitation forecasts: some experimental results.

Journal Article Monthly Weather Review · January 1, 1985 This paper summarizes the results of an experiment in which National Weather Service forecasters formulated probabilistic quantitative precipitation forecasts (GPFs) during a 17-month period in 1981-82. These forecasts expressed the likelihood that certain ... Full text Cite

Probability Forecasting in Meterology

Journal Article Journal of the American Statistical Association · September 1984 Full text Cite

Probability forecasting in meteorology

Journal Article Journal of the American Statistical Association · January 1, 1984 Efforts to quantify the uncertainty in weather forecasts began more than 75 years ago, and many studies and experiments involving objective and subjective probability forecasting have been conducted in meteorology in the intervening period. Moreover, the U ... Full text Cite

Analysis of alternative national ambient carbon monoxide standards

Journal Article Management Science · January 1, 1984 A risk assessment model is developed to relate adverse health effects to alternative carbon monoxide standards. The analysis requires information in the form of available data and expert judgments concerning factors such as ambient CO level, human exposure ... Full text Cite

RISK ASSESSMENT MODEL FOR THE STUDY OF ALTERNATIVE NATIONAL AMBIENT CARBON MONOXIDE STANDARDS.

Journal Article Proceedings Annual Meeting Air Pollution Control Association · December 1, 1983 Cite

Progression of myopia in youth: age of cessation.

Journal Article American journal of optometry and physiological optics · August 1983 Patient records of young myopes were collected from three optometry practices. An index of the age at which increases of myopia in young people cease was derived using four different graphical and statistical methods. The results suggest that myopia stops ... Full text Cite

The Combination of Forecasts

Journal Article Journal of the Royal Statistical Society. Series A (General) · 1983 Cite

The value of climate information: A decision‐analytic approach

Journal Article Journal of Climatology · January 1, 1983 A decision‐analytic approach to the problem of assessing the value of climate information is presented and an application of this methodology to a decision‐making problem involving the use of climate information is described. First, decision analysis is di ... Full text Cite

AVERAGES OF FORECASTS: SOME EMPIRICAL RESULTS.

Journal Article Management Science · January 1, 1983 An alternative to using a single forecasting method is to average the forecasts obtained from several methods. In this paper the authors investigate empirically the impact of the number and choice of forecasting methods on the accuracy of simple averages. ... Full text Cite

Progression of myopia in youth: Age of cessation

Journal Article Optometry and Vision Science · January 1, 1983 Patient records of young myopes were collected from three optometry practices. An index of the age at which increases of myopia in young people cease was derived using four different graphical and statistical methods. The results suggest that myopia stops ... Cite

Subjective Probabilistic Tornado Forecasts: Some Experimental Results

Journal Article Monthly Weather Review · September 1982 Full text Cite

State of the Art: RESEARCH DIRECTIONS IN DECISION MAKING UNDER UNCERTAINTY

Journal Article Decision Sciences · January 1, 1982 This paper considers the modeling of decision‐making problems under uncertainty, indicating current gaps in knowledge and promising research directions. Technical details are omitted, and no attempt is made to review past work since excellent recent review ... Full text Cite

LEARNING, EXPERIMENTATION, AND THE OPTIMAL OUTPUT DECISIONS OF A COMPETITIVE FIRM.

Journal Article Management Science · January 1, 1982 This study considers the effect of learning from experience on the output decisions of a perfectly competitive firm faced with the demand uncertainty. Specifically, a Bayesian framework for expectations formation and demand forecasting by a perfectly compe ... Full text Cite

Assessing the value of frost forecasts to orchardists: a dynamic decision-making approach.

Journal Article Journal of Applied Meteorology · January 1, 1982 The methodology of decision analysis is used to investigate the economic value of frost forecasts to orchardists. First, the fruit-frost situation and previous studies of the value of minimum temperature forecasts in this context are described. Then, after ... Full text Cite

Combining Probability Distributions from Dependent Information Sources

Journal Article Management Science · April 1981 Inferences or decisions in the face of uncertainty should be based on all available information. Thus, when probability distributions for an uncertain quantity are obtained from experts, models, or other information sources, these distributions sh ... Full text Cite

Risk assessment: consulting the experts.

Journal Article Environmental Professional · January 1, 1981 A step-by-step procedure for assessing health risks of environmental pollutants is described, and how risk assessment can be used in an evaluation model for selecting alternative air quality standards is discussed.-from Authors ... Cite

RISK SHARING AND GROUP DECISION MAKING.

Journal Article Management Science · January 1, 1981 In a decision-making problem where a group will receive an uncertain payoff which must be divided among the members of the group, the ultimate payoff of interest is the vector of individual payoffs received by the members of the group. In this study, prefe ... Full text Cite

Informational Differences Between Limit and Market Orders for a Market Maker

Journal Article Journal of Financial and Quantitative Analysis · January 1, 1981 Full text Cite

Misinterpretations of precipitation probability forecasts ( Eugene, Oregon).

Journal Article · December 1, 1980 Previous studies have suggested that the general public misinterprets probability of precipitation (PoP) forecasts. Summarizes a study of 79 residents of Eugene, Oregon who completed a questionnaire designed to investigate their understanding of an attitud ... Cite

Performance-Based Incentive Plans

Journal Article Management Science · November 1980 Incentive plans are an integral part of management control since incentives as measures of recognition of performance are significant motivating factors for corporate executives. In this paper we describe how such incentive plans can be devised. W ... Full text Cite

Competitive Bidding with Dependent Value Estimates

Journal Article Operations Research · June 1980 A bidding situation in which there is uncertainty about the value of the item of interest is modeled. The uncertainty is modeled in probabilistic terms, and the model allows the errors of estimation (the differences between expected values and the ... Full text Cite

Interactive Elicitation of Opinion for a Normal Linear Model

Journal Article Journal of the American Statistical Association · 1980 Cite

Interactive elicitation of opinion for a normal linear model

Journal Article Journal of the American Statistical Association · January 1, 1980 This article describes the mathematical theory underlying an interactive computer program for eliciting the hyperparameters of a subjective conjugate distribution for the multiple linear regression model with the usual normal error structure. Although the ... Full text Cite

Misinterpretations of precipitation probability forecasts ( Eugene, Oregon).

Journal Article undefined · January 1, 1980 Previous studies have suggested that the general public misinterprets probability of precipitation (PoP) forecasts. Summarizes a study of 79 residents of Eugene, Oregon who completed a questionnaire designed to investigate their understanding of an attitud ... Cite

Misinterpretations of precipitation probability forecasts ( Eugene, Oregon).

Journal Article Bulletin American Meteorological Society · January 1, 1980 Summarizes a study of 79 residents of Eugene, Oreg., who completed a questionnaire designed to investigate their understanding of and attitude toward precipitation probability forecasts. Results indicate that the event in question frequently is misundersto ... Cite

Warner’s randomized response model: A Bayesian approach

Journal Article Journal of the American Statistical Association · January 1, 1979 In randomized response sampling, prior information is of particular value because the randomization effectively reduces the amount of sample information. Warner’s model with a beta prior distribution for the proportion of interest yields posterior distribu ... Full text Cite

The use of probabilities in forecasts of maximum and minimum temperatures.

Journal Article Meteorological Magazine · January 1, 1979 Subjective probabilistic temperature forecasting is studied. Alternative summary measures of a forecaster's probability distribution of temperature are considered, and 'credible intervals' are suggested as a suitable choice for operational forecasts of thi ... Cite

Problabilistic temperature forecasts: the case for an operational program.

Journal Article Bulletin American Meteorological Society · January 1, 1979 The case for an operational program involving the formulation and dissemination of probabilistic temperature forecasts is presented. First, the need for information concerning the uncertainity in temperature forecasts is discussed, and examples of formal a ... Cite

Subjective quantification of uncertainty in tornado forecasts: Some experimental results.

Journal Article undefined · January 1, 1979 An experiment was conducted in which NWS forecasters at the National Severe Storms Forecast Center (NSSFC) expressed forecasts of tornado occurrence and intensity in probabilistic terms. These forecasts were formulated in conjunction with the regular outlo ... Cite

Statisticians Can Matter: Comment

Journal Article The American statistician · 1978 Cite

Comment

Journal Article American Statistician · January 1, 1978 Full text Cite

ROLE OF ATTITUDE TOWARD RISK IN STRICTLY COMPETITIVE DECISION-MAKING SITUATIONS.

Journal Article undefined · January 1, 1978 The impact of decision makers' attitudes toward risk has been studied extensively in the context of noncompetitive decision making but not in the context of competitive decision making. A study is made of the effects of the utility functions of the players ... Full text Cite

Reliability of Subjective Probability Forecasts of Precipitation and Temperature

Journal Article Journal of the Royal Statistical Society: Series C (Applied Statistics) · 1977 Cite

Nonstationarity and Portfolio Choice

Journal Article Journal of Financial and Quantitative Analysis · 1976 Cite

OPTIMAL SPECULATION AGAINST AN EFFICIENT MARKET

Journal Article Journal of Finance · January 1, 1976 Full text Cite

Nohstationarity and portfolio choice

Journal Article Journal of Financial and Quantitative Analysis · January 1, 1976 Full text Cite

SCORING RULES FOR CONTINUOUS PROBABILITY DISTRIBUTIONS.

Journal Article Management Science · January 1, 1976 Personal, or subjective, probabilities are used as inputs to many inferential and decision-making models, and various procedures have been developed for the elicitation of such probabilities. Included among these elicitation procedures are scoring rules, w ... Full text Cite

Personal probabilities of probabilities

Journal Article Theory and Decision · May 1, 1975 By definition, the subjective probability distribution of a random event is revealed by the ('rational') subject's 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 ... Full text Cite

A BAYESIAN MODEL FOR PORTFOLIO SELECTION AND REVISION

Journal Article Journal of Finance · January 1, 1975 Full text Cite

Cognitive Processes and the Assessment of Subjective Probability Distributions: Comment

Journal Article Journal of the American Statistical Association · 1975 Cite

Comment

Journal Article Journal of the American Statistical Association · January 1, 1975 Full text Cite

Probabilistic tornado forecasts: some experimental results.

Journal Article undefined · January 1, 1975 Some preliminary results of an experiment in which NWS forecasters at the National Severe Storms Forecast Center (NSSFC) expressed forecasts of tornado occurrence and intensity in probabilistic terms are described. (from paper) (REF CONTD)(Omaha, Nebraska, ... Cite

Probability Forecasts: a Survey of National Weather Service Forecasters

Journal Article Bulletin of the American Meteorological Society · December 1974 Full text Cite

Bayesian point estimation and prediction

Journal Article Annals of the Institute of Statistical Mathematics · December 1, 1974 In the Bayesian viewpoint, point estimation and prediction are treated from a decision-making standpoint. If a loss function can be determined which associates a loss with every possible error of estimation or prediction, then the optimal estimator or pred ... Full text Cite

Credible Interval Temperature Forecasting: Some Experimental Results

Journal Article Monthly Weather Review · November 1974 Full text Cite

Bayesian Models for Forecasting Future Security Prices

Journal Article Journal of Financial and Quantitative Analysis · 1973 Cite

Subjective Probability Forecasting of Temperature: Some Experimental Results

Journal Article Bulletin of the International Statistical Institute · 1973 Cite

Bayesianism: Its Unifying Role for Both the Foundations and the Applications of Statistics: Comments

Journal Article Bulleting of the International Statistical Institute · 1973 Cite

Experiments in the laboratory and the real world

Journal Article Organizational Behavior and Human Performance · January 1, 1973 The age-old question of the generalizability of the results of experiments that are conducted in artificial laboratory settings to more realistic inferential and decision-making situations is considered in this paper. Conservatism in probability revision p ... Full text Cite

Information Aggregation in Probabilistic Prediction

Journal Article IEEE Transactions on Systems Man and Cybernetics · January 1, 1973 Full text Cite

The Determination of Partial Moments

Journal Article Management Science · November 1972 In statistical decision theory, computations often involve the partial moments of a random variable. Several methods for determining partial moments are discussed, including direct calculation, the use of general formulas which apply to entire fam ... Full text Cite

Comment

Journal Article Journal of the American Statistical Association · January 1, 1972 Full text Cite

A decision-theoretic approach to interval estimation

Journal Article Journal of the American Statistical Association · January 1, 1972 Under an appropriate loss function, interval estimation may be regarded as a Bayesian decision-making procedure in which the objective is to find an interval that minimizes expected loss. For various loss functions, the behavior of the optimal interval is ... Full text Cite

On the choice of a consensus distribution in Bayesian analysis

Journal Article Organizational Behavior and Human Performance · January 1, 1972 Four methods of arriving at a consensus distribution in Bayesian analysis are described (weighted-average, natural-conjugate, feedback and reassessment, and group reassessment). The weighted-average and natural-conjugate methods are compared empirically in ... Full text Cite

Forecasters and Probability Forecasts: Some Current Problems

Journal Article Bulletin of the American Meteorological Society · April 1971 Full text Cite

Forecasters and Probability Forecasts: the Responses to a Questionnaire

Journal Article Bulletin of the American Meteorological Society · March 1971 Full text Cite

Probabilistic Prediction: Some Experimental Results

Journal Article Journal of the American Statistical Association · 1971 Cite

Probabilistic prediction: Some experimental results

Journal Article Journal of the American Statistical Association · January 1, 1971 This article concerns a study in which personal probability assessments regarding the outcomes of football games were obtained. The results reported here, which include a detailed investigation of the assessments, an evaluation of the assessments in an inf ... Full text Cite

Intuitive bayesian point estimation

Journal Article Organizational Behavior and Human Performance · January 1, 1970 This paper presents the results of an experiment designed to investigate the relationship between intuitive Bayesian point estimates and theoretically optimal Bayesian point estimates for various probability distributions (normal distributions) and loss fu ... Full text Cite

NONLINEAR UTILITY AND THE PROBABILITY SCORE

Journal Article Journal of Applied Meteorology · January 1, 1970 Proper scoring rules, such as the probability score, are based (in part) upon the assumption that the assessor's utility function is linearly related to the score. The effects of two nonlinear utility functions, one representing a '%'risk-taker'%' and one ... Cite

Scoring rules in probability assessment and evaluation

Journal Article Acta Psychologica · January 1, 1970 The purpose of this paper is to briefly discuss some important current questions and problems related to the use of scoring rules (SRs) both in connection with the actual assessment of probabilities and with the evaluation of probability forecasts and prob ... Full text Cite

Scoring Rules and the Evaluation of Probability Assessors

Journal Article Journal of the American Statistical Association · 1969 Cite

Scoring Rules and the Evaluation of Probability Assessors

Journal Article Journal of the American Statistical Association · January 1, 1969 The personalistic theory of probability prescribes that personal probability assessments to be used in decision-making situations should correspond with the assessor's judgments. A payoff function which depends on the assessor's stated probabilities and on ... Full text Cite

The Consensus of Subjective Probability Distributions

Journal Article Management Science · October 1968 “‘But we can't agree whether A or B is correct,' he concluded, ‘and so we're collecting expert opinions, weighting them appropriately, and programming WESCAC to arbitrate the whole question.’” (John Barth, Giles Goat-Boy, p. 664.) Full text Cite

“Good” Probability Assessors

Journal Article Journal of Applied Meteorology · October 1968 Full text Cite

The Assessment of Prior Distributions in Bayesian Analysis

Journal Article Journal of the American Statistical Association · 1967 Cite

The Quantification of Judgment: Some Methodological Suggestions

Journal Article Journal of the American Statistical Association · 1967 Cite

The Assessment of Prior Distributions in Bayesian Analysis

Journal Article Journal of the American Statistical Association · January 1, 1967 In the Bayesian framework, quantified judgments about uncertainty are an indispensable input to methods of statistical inference and decision. Ultimately, all components of the formal mathematical models underlying inferential procedures represent quantifi ... Full text Cite

The Quantification of Judgment: Some Methodological Suggestions

Journal Article Journal of the American Statistical Association · January 1, 1967 The personalistic theory of probability prescribes that a person should use personal probability assessments in decision-making and that these assessments should correspond with his judgments. Since the judgments exist solely in the assessor's mind, there ... Full text Cite