Edward S. Epstein

Verification of Probabilistic Predictions: A Brief Review

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.

A Note on Probability Forecasts and “Hedging”

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.

Detecting Climate Change

Abstract The likelihood ratio of the data for a hypothesis of some change, relative to the hypothesis of no change, is a suitable statistical measure for the detection of climate change. Likelihood ratios calculated on the basis of Angell and Korshovers (1977) global mean temperature, updated through 1980, do not show convincing evidence of recent climate change. It is possible to calculate probabilities of obtaining future values of likelihood ratios, depending on the postulated future climate change. A modest but significant climate change, such as that expected to occur from an increase of atmospheric carbon dioxide, is likely to be detected from global mean surface temperatures within ten years. The joint behavior of the troposphere and stratosphere is more likely to discriminate between climate change and no change than are surface temperatures. In this case, a climate change that can be attributed to carbon dioxide increase should be detectable by 1986.

Application of Two-Dimensional Spectral Analysis to the Quantification of Satellite Cloud Photographs

Abstract Pictures from TIROS have revealed that cumuliform clouds over the ocean quite often occur in the form of a complex pattern with lines and cells of horizontal dimensions in the range of 20 to 100 miles and with various orientations seemingly superimposed. Gross features of these patterns such as the horizontal dimensions and orientation which are predominant over particular areas should prove very useful as indicators of the prevailing meteorological conditions. A two-dimensional extension of the familiar power spectrum analysis has been applied to the TIROS photographs. The object of the analysis is to identify and quantify the statistically preferred dimensions and orientations of the cloud patterns. Digital data are derived from the photographs by adopting a simple 5-level gray scale of cloud brightness. A Monte Carlo technique has yielded estimates of the reliability of the statistical analysis. Results from these analyses have revealed patterns which tended to be obscured by the more dominant...