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Allan H. Murphy
and
Robert L. Winkler

Abstract

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Edward S. Epstein
and
Allan H. Murphy

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Allan H. Murphy
and
Jack C. Thompson

Abstract

t has been shown previously that ordinal relationships between measures of the accuracy and value ofprobability forecasts do not exist, in general, in N-state (N > 2) situations. Some implications of this resultare illustrated by comparing the accuracy and value of such forecasts in a realistic decision-making situation-a three-action, three-state situation involving the protection of a fruit orchard against frosts and freezes.Geometrical interpretations of the forecasts and measures are described and then used to investigate the existence of ordinal relationships in this so-called fruit-frost situation. The results indicate, as expected, thatan increase in forecast accuracy can lead to a decrease in forecast value. Some generalizations and speculations related to the existence and nonexistence of such ordinal relationships are presented.

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Allan H. Murphy
and
Edward S. Epstein

Abstract

The evaluation process is considered in some detail with particular reference to probabilistic predictions. The process consists of several ordered steps at each of which elements (of the process) are identified. Consideration of the purposes leads to the identification of two distinct forms of evaluation: operational evaluation concerned with the value of predictions to the user and empirical evaluation, or verification, concerned with the perfection of predictions, i.e., the association between predictions and observations. Attributes, i.e., desirable properties, of predictions are defined with reference to these purposes, and a number of measures of the attributes for empirical evaluation are considered. An artificial example of comparative verification in which different measures appear to yield contradictory results is used to demonstrate the importance of, and need for, a careful analysis of the evaluation process.

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Allan H. Murphy
and
Edward S. Epstein

Abstract

The consideration of a maxim and a statement, both of which are concerned with “hedging” on the part of meteorologists who prepare probability forecasts, leads to the identification of a property which all proper scoring systems for such forecasts should possess. A scoring system, to be proper, should encourage the meteorologist to make his probabilities correspond to his true beliefs. The conditions which a proper scoring system must satisfy are formulated in mathematical terms. Several existing scoring systems are examined to ascertain whether or not the systems are proper.

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Robert L. Winkler
and
Allan H. Murphy

Abstract

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 representing a “risk-avoider,” on an assessor's probability forecasts are considered. The results indicate that factors other than the expected score, e.g., the variance of the score, may be relevant for probability assessment. In general, a “risk-taker” “hedges” toward a categorical forecast, while a “risk-avoider” “hedges” away from a categorical forecast. The implications of these results for the process of probability assessment are briefly discussed.

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Robert L. Winkler
and
Allan H. Murphy

Abstract

Since a meteorologist's predictions are subjective, a framework for the evaluation of meteorological probability assessors must be consistent with the theory of subjective probability. Such a framework is described in this paper. First, two standards of “goodness,” one based upon normative considerations and one based upon substantive considerations, are proposed. Specific properties which a meteorologist's assessments should possess are identified for each standard. Then, several measures of “goodness,” or scoring rules, which indicate the extent to which such assessments possess certain properties, are described. Finally, several important uses of these scoring rules are considered.

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Paul R. Julian
and
Allan H. Murphy

Recent developments in six areas of statistical meteorology are described and the importance of interdisciplinary research in these areas is indicated. The areas are stochastic-dynamic prediction, assimilation of observed data, time-series analysis, statistical weather forecasting, probability forecasting, and precipitation modification statistics. Several problems are identified within each area and the need for further interdisciplinary research to solve these problems is emphasized.

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Allan H. Murphy
and
Barbara G. Brown

This paper reports some results of a study in which two groups of individuals—undergraduate students and professional meteorologists at Oregon State University—completed a short questionnaire concerning their interpretations of terminology commonly used in public weather forecasts. The questions related to terms and phrases associated with three elements: 1) cloudiness—fraction of sky cover; 2) precipitation—spatial and/or temporal variations; and 3) temperature—specification of intervals.

The students' responses indicate that cloudiness terms are subject to wide and overlapping ranges of interpretation, although the interpretations of these terms correspond quite well to National Weather Service definitions. Their responses to the precipitation and temperature questions reveal that some confusion exists concerning the meaning of spatial and temporal modifiers in precipitation forecasts and that some individuals interpret temperature ranges in terms of asymmetric intervals. When compared to the students' responses, the meteorologists' responses exhibit narrower ranges of interpretation of the cloudiness terms and less confusion about the meaning of spatial/temporal precipitation modifiers.

The study was not intended to be a definitive analysis of public understanding of forecast terminology. Instead, it should be viewed as a primitive form of the type of forecast-terminology study that must be undertaken in the future. Some implications of this investigation for future work in the area are discussed briefly.

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Allan H. Murphy
and
Barbara G. Brown

Worded forecasts, which generally consist of both verbal and numerical expressions, play an important role in the communication of weather information to the general public. However, relatively few studies of the composition and interpretation of such forecasts have been conducted. Moreover, the studies that have been undertaken to date indicate that many expressions currently used in public forecasts are subject to wide ranges of interpretation (and to misinterpretation) and that the ability of individuals to recall the content of worded forecasts is quite limited. This paper focuses on forecast terminology and the understanding of such terminology in the context of short-range public weather forecasts.

The results of previous studies of forecast terminology (and related issues) are summarized with respect to six basic aspects or facets of worded forecasts. These facets include: 1) events (the values of the meteorological variables): 2) terminology (the words used to describe the events); 3) words versus numbers (the use of verbal and/or numerical expressions); 4) uncertainty (the mode of expression of uncertainty); 5) amount of information (the number of items of information); and 6) content and format (the selection of items of information and their placement). In addition, some related topics are treated briefly, including the impact of verification systems, the role of computer-worded forecasts, the implications of new modes of communication, and the use of weather forecasts.

Some conclusions and inferences that can be drawn from this review of previous work are discussed briefly, and a set of recommendations are presented regarding steps that should be taken to raise the level of understanding and enhance the usefulness of worded forecasts. These recommendations are organized under four headings: 1) studies of public understanding, interpretation, and use; 2) management practices; 3) forecaster training and education; and 4) public education.

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