Should Scoring Rules Be 'Effective'?

Article Abstract:

A scoring rule is a reward function for eliciting or evaluating forecasts expressed as discrete or continuous probability distributions. A rule is strictly proper if it encourages the forecaster to state his true subjective probabilities, and effective if it is associated with a metric on the set of probability distributions. Recently, the property of effectiveness (which is stronger than strict properness) has been proposed as a desideratum for scoring rules for continuous forecasts, for reasons of 'monotonicity' in keeping the forecaster close to his true probabilities, since in practice the forecast must be chosen from a low-dimensional set of 'admissible' distributions. It is shown in this paper that what effectiveness implies, beyond strict properness, is not a monotonicity property but a transitivity property, which is difficult to justify behaviorally. The logarithmic scoring rule is shown to violate the transitivity property and hence is not effective. The L subscript 1 and L subscript (infinity) metrics are shown to allow no effective scoring rules. Some potential difficulties in interpreting admissible forecasts are also discussed. (Reprinted by Permission of Publisher.)

Evaluation, Efficiency, Probability

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Effective Scoring Rules for Probabilistic Forecasts

Article Abstract:

Decision makers using forecasts need assurance that experts produce a forecast that reflects the expert's best judgement. Also, a decision maker needs a way, after the fact, of judging the quality of the forecast. A rule which assigns to the expert some score based on his forecast deals with both problems. The expert will attempt to maximize his score. It is important to keep discrepancy between forecast and reality small. A scoring rule is effective if the forecaster's expected score is a decreasing function of the distance between the forecast and reality. Foreign exchange rate forecasting is used as a practical example.

Management science, Modeling, Data modeling software, Decision Making

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Strategies for the probabilistic lot-sizing problem with service-level constraints

Article Abstract:

A stochastic-demand version of the single-stage lot-sizing problem is formulated, with time-varying demand. A service-level constraint is also incorporated on the likelihood of a stock-out. Three strategies are examined: static uncertainty, dynamic uncertainty, and static-dynamic uncertainty. Relationships between the strategies are suggested, and several aspects of rolling horizon production planning are considered. It is argued that the static uncertainty approach is the most straightforward to alter and 'roll along' as new demands become apparent.

Research, Methods, Usage, Stochastic analysis, Economic lot size, Stochastic programming

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