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Compares the results from the statistical Rule of Three method with those from a Bayesian approach with non-informative and informative priors in a zero-numerator problem. Analysis of risk associated with new contrast agent; Role of informative priors in zero-numerator problems; False-positive rate.

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.S. National Weather Service (NWS) initiated a nationwide program in 1965 in which precipitation probability forecasts were formulated on an operational basis and routinely disseminated to the general public. In addition, the NWS now prepares objective probability forecasts for many variables, using statistical procedures. Hence probability forecasting in meteorology is unique in that very large sets of probability forecasts that have been subjected to detailed evaluation are available. This article has four objectives: (a) to review the history of probability forecasting in meteorology to acquaint statisticians with this body of literature; (b) to describe recent methodological, experimental, and operational activities in this field; (c) to examine current issues in probability forecasting; and (d) to discuss briefly the relationship between probability forecasting in meteorology and probability forecasting in other fields. Results of operational and experimental weather forecasting programs are presented, methods of verifying and evaluating probability forecasts in common use in meteorology are discussed, and an extensive list of references is provided. [ABSTRACT FROM AUTHOR]

Forecasting errors fall in two clearly different categories: (a) the residual errors from fitting a model to the available data and (b) the post-sample forecasting errors. The emphasis of statistical theory and forecasting methodology has been on model fitting errors, even though the greatest concern in applied work should be with post-sample errors, The purpose of this paper is to investigate empirically sampling distributions of post-sample forecasting errors. The characteristics of such distributions are studied and compared with characteristics of distributions of model fitting errors. The discrepancies between characteristics of model fitting and post-sample errors are quite large and somewhat variable, [ABSTRACT FROM AUTHOR]

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 sensitivity, or instability, of the estimated weights used to generate the combined forecast. The intent of this paper is to look at this instability via graphs and the sampling distribution of the weights. Results are developed for the combination of two forecasts and extended to the m-forecast case by viewing the m-forecast case as a sequence of two-forecast combinations. [ABSTRACT FROM AUTHOR]

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 the information. Prior research in this area has relied primarily on the use of historical data as a basis for modeling the information sources. We develop a Bayesian framework that a decision maker can use to encode subjective knowledge about the information sources in order to aggregate point estimates of an unknown quantity of interest. This framework features a highly flexible environment for modeling the probabilistic nature and interrelationships of the information sources and requires straightforward and intuitive subjective judgments using proven decision-analysis assessment techniques. Analysis of the constructed model produces a posterior distribution for the quantity of interest. An example based on health risks due to ozone exposure demonstrates the technique. [ABSTRACT FROM AUTHOR]

An alternative to using a single forecasting method is to average the forecasts obtained from several methods. In this paper we investigate empirically the impact of the number and choice of forecasting methods on the accuracy of simple averages. It is concluded that the forecasting accuracy improves, and that the variability of accuracy among different combinations decreases, as the number of methods in the average increases. Thus, combining forecasts seems to be a reasonable practical alternative when, as is often the case, a "true" model of the data-generating process or a single "best" forecasting method cannot be or is not, for whatever reasons, identified. [ABSTRACT FROM AUTHOR]

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 methods are heuristic, they are shown to produce hyperparameter estimates satisfying the constraints satisfied by the hyperparameters themselves. An application is given to the problem of predicting the time to fatigue failure of an asphalt-concrete road as a function of several design variables concerning the road. [ABSTRACT FROM AUTHOR]

Discusses the author's views on an article about the time series model forecasts of count observations. Notion of learning about nonstationarity processes; Discussion of Bayesian and non-Bayesian analysis that touched on foundational issues; Nature of randomness.

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 inferential context and in a decision-theoretic context, and a discussion of the performance of a consensus, show that methods such as scoring rules and bets are useful in leading individuals to make careful probability assessments. Considerable variability existed among subjects, however, with predictions determined by mechanical schemes and by the organized betting market proving superior to those of many of the subjects. [ABSTRACT FROM AUTHOR]

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 the event which actually occurs may be used (1) to keep the assessor honest or (2) to evaluate the assessor. It is shown that with the exception of a logarithmic payoff function, these two uses of payoff functions for assessors are not compatible. This conflict is explained in terms of the differences in the situations facing the assessor and the evaluator (the user of the probabilistic predictions). [ABSTRACT FROM AUTHOR]

The article presents information on various developments related to statistics. Although some work concerning the assessment of subjective probabilities has been reported in the statistical literature in recent years, much of this work has been conducted by statisticians rather than by psychologists. Most statisticians are probably not aware of the voluminous literature on the psychology of judgment. Clearly, psychological factors are relevant and important in the assessment of subjective probabilities, and psychologists tend to approach the topic from a somewhat different viewpoint than statisticians, as might be expected. The area of cognitive processes may have important implications for probability assessment, and further work needs to be done to investigate such implications. Of course, the assessment of probabilities forces people to recognize uncertainty explicitly and to quantify it. The lack of encouragement, together with the related lack of familiarity, sometimes causes negative reactions to statements involving probability. For example, the decision of the U.S. National Weather Service a decade ago to issue precipitation probabilities to the public on a regular basis drew some negative response.