Scoring Rules, Generalized Entropy, and Utility Maximization

Jose, Victor Richmond R.; Nau, Robert F.; Winkler, Robert L.

doi:10.1287/opre.1070.0498

Cited by 74 publications

(78 citation statements)

References 35 publications

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“…As for the skill score, it has the disadvantage of not being strictly proper. Jose et al (2008) provide a rich set of strictly proper scoring rules, the power and pseudospherical families, that can incorporate the notion of a baseline distribution but do not take into account any ordering of the states.…”

Section: Summary and Discussionmentioning

confidence: 99%

“…Example 1. Two rich families of strictly proper rules are the power and pseudospherical families of scoring rules with parameter (Jose et al 2008):…”

Section: Scoring Rulesmentioning

confidence: 99%

“…This canonical form of the linear-risk-tolerance utility function, which is introduced by Jose et al (2008), has the following key properties: (i) it is a continuous function of on the entire real line for fixed x, (ii) the forecaster's marginal utility of wealth is normalized to be 1 at x = 0 for all , and (iii) the forecaster's local risk tolerance at wealth x is normalized to be 1 + x. In this context, different values of represent different risk attitudes on the part of a decision maker who must act on the basis of the forecast and who wishes to reward the forecaster in proportion to the decision maker's own utility gain or loss.…”

Section: Scoring Rulesmentioning

confidence: 99%

“…One way to address this issue is to create asymmetric strictly proper rules that are related to a baseline distribution while retaining the property of strict propriety, as done in Winkler (1994) and Jose et al (2008) for unordered spaces. Using the construction in the previous section, we can create similar scores for ordered state spaces.…”

Section: Scoring Rules With Baselinesmentioning

confidence: 99%

“…In a location where precipitation occurs on average only 5% of the time, a baseline probability of one-half seems inappropriate. In the case of scoring rules for unordered categories, this issue has been addressed by looking at "asymmetric" scoring rules that allow for the consideration of a nonuniform baseline distribution (Winkler 1994, Jose et al 2008. But for spaces where outcomes are ordered, no algorithm has been developed that provides for the creation of a rule with any desired baseline distribution.…”

Section: Introductionmentioning

confidence: 99%

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Sensitivity to Distance and Baseline Distributions in Forecast Evaluation

2009

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S coring 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 distribution is desired. Scoring rules typically studied in the literature and used in practice do not take account of any ordering of events, and they evaluate probabilities relative to a default baseline distribution. In this paper, we construct rich families of scoring rules that are strictly proper (thereby encouraging truthful reporting), are sensitive to distance (thereby taking into account ordering of events), and incorporate a baseline distribution relative to which the value of a forecast is measured. In particular, we extend the power and pseudospherical families of scoring rules to allow for sensitivity to distance, with or without a specified baseline distribution.

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Section: Summary and Discussionmentioning

confidence: 99%

“…Example 1. Two rich families of strictly proper rules are the power and pseudospherical families of scoring rules with parameter (Jose et al 2008):…”

Section: Scoring Rulesmentioning

confidence: 99%

Section: Scoring Rulesmentioning

confidence: 99%

Section: Scoring Rules With Baselinesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Sensitivity to Distance and Baseline Distributions in Forecast Evaluation

2009

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Scoring Rules

Winkler¹,

Jose²

2011

Wiley Encyclopedia of Operations Research and Management Science

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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 are valuable in evaluating how “good” probabilities are in light of what happens, and they also provide incentives for careful elicitation of probabilities. We discuss basic properties of scoring rules, present families of scoring rules that are useful under various conditions, and discuss some related issues.

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Well‐Calibrated Forecasts

Gross¹

2017

Wiley StatsRef: Statistics Reference Online

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In meteorology, finance, and economics, predictions for the next period are regularly published for the consumer of such information. In weather prediction of temperature, rain occurrence, or rainfall amount, forecasts are made for the next day based on historical information of actual temperatures, other associated meteorological variables, and predictions already made, up to, and including, the present. Similar predictions are made in financial predictions of the Dow Jones Industrial Average (DJIA) increase or decrease, or its actual value next month, based on past predictions and historical data available up to the current period. We review the development of the concept of calibration, the long run agreement between a regular repeated prediction and the actual quantity, in the prediction of probabilities of future events and in the prediction of entire distributions of future continuous random variables. Finally, the issue of combining several forecasts, or forecasting model predictions, in both event probability and continuous distribution, is reviewed, and the use of transformations of the weighted average prediction is described. We also briefly describe more recent results pertaining to the sharpness of well‐calibrated predictions.

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Scoring Rules, Generalized Entropy, and Utility Maximization

Cited by 74 publications

References 35 publications

Sensitivity to Distance and Baseline Distributions in Forecast Evaluation

Sensitivity to Distance and Baseline Distributions in Forecast Evaluation

Scoring Rules

Well‐Calibrated Forecasts

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