Risk and Energy Systems: Deterministic versus Probabilistic Models

At the conference on "Energy Systems" that was held in Baden July 17-20, 1973, the discussion regarding models and model-building was, for the most part, limited to deterministic models. Only at the end of the conference, in the discussion of "risk and reliability problems," was the question of deterministic models versus probabilistic models brought up. The brief discussion that ensued indicated that there exists some hesitancy on the part of model builders in the energy systems area to include probabilities in their models. Such model builders recognize the presence of uncertainty in the situations they are modeling, but they appear to feel uncomfortable about formally representing this uncertainty in terms of probabilities. This uncomfortable feeling may be due to several factors, including a lack of familiarity with probabilistic models, a question about the source of probabilities for probabilistic models, a feeling that deterministic models are perfectly adequate, and a concern that probabilistic models regarding energy systems would be too complex and difficult to handle. Unfortunately, because the question of deterministic models versus probabilistic models arose so late in the conference, adequate time was not available for a full discussion of the question. Of course, a full discussion would require several days with many papers and presentations. Since that is not immediately feasible, this paper represents an attempt to present an overview of some of the issues that are involved in the question of deterministic models versus probabilistic models

Nonstationarity and Portfolio Choice

In this paper some effects of nonstationary parameters upon inferences and decisions in portfolio analysis are investigated. A Bayesian inferential model with nonstationary parameters is presented and is applied to the problem of portfolio choice. For this model, nonstationarity 1) implies greater uncertainty about future returns; 2) implies that in forecasting future returns, recent returns should receive more weight than not-so-recent returns; 3) restricts the amount of information that can be obtained about future values of the parameters of interest; 4) shifts investment among risky securities and from risky securities to risk-free securities; and 5) yields optimal portfolios with smaller expected returns than corresponding optimal portfolios in the stationary case

Point and Area Precipitation Probability Forecasts: Some Experimental Results

An experiment was conducted at the National Weather Service Forecast Office in St. Louis, Missouri, to investigate the ability of forecasters to differentiate among different points in a forecast area with regard to the likelihood of the occurrence of measurable precipitation and the relative ability of forecasters to make point and area precipitation probability forecasts. On each forecasting occasion in the experimental period (November 1972 to March 1973), the forecasters made an average point probability forecast for the St. Louis metropolitan area, point probability forecasts for five specific points in the area, an are a probability forecast, and an expected areal coverage forecast. The results indicate that the forecasters did not differentiate among the five points very often, but that this absence of differences among the point probabilities was justified by the lack of variability exhibited by the observations of precipitation occurrence at these points during the experimental period. Evaluations of the average point probability forecasts, individual point probability forecasts, and expected areal coverage forecasts reveal that these forecasts were quite reliable and accurate and that they were also internally consistent. The area probability forecasts, however, tended not to be consistent with the other forecasts, and the average area probability forecast was considerably lower than the relative frequency of occurrence of precipitation "somewhere in the area." The implications of these results for precipitation probability forecasting in meteorology are briefly discussed

Credible Interval Temperature Forecasting: Some Experimental Results

This paper describes the results of an experiment involving credible interval temperature forecasts. A credible interval is an interval of values of the variable of concern, in this case maximum or minimum temperature, accompanied by a probability which expresses a forecaster's "degree of belief" that the temperature will fall in the given interval. The experiment was designed to investigate the ability of forecasters to express the uncertainty inherent in their temperature forecasts in probabilistic terms and to compare two approaches (variable-width and fixed-width intervals) to credible interval temperature forecasting. Four experienced weather forecasters participated in the experiment, which was conducted at the National Weather Service Forecast Office in Denver, Colorado. Two forecasters made variable-width, fixed-probability forecasts using 50% and 75% intervals, while the other two forecasters made fixed-width, variable-probability forecasts using 5 degree F and 9 degree F intervals. On each occasion the forecasters first determined a median, and the variable-width and fixed-width intervals were then centered at the median in terms of probability and width, respectively. The results indicate that, overall, the medians determined by the forecasters were good point forecasts of maximum and minimum temperatures. Further, a comparison of the average errors for the forecasters' medians with the average errors for the medians derived from climatology reveals that the forecasters were able to improve greatly upon climatology. The variable-width credible intervals were very reliable in the sense that the observed relative frequencies corresponded very closely to the forecast probabilities. Moreover, the variable-width intervals were more reliable and much more precise than the corresponding forecasts derived from climatology. The fixed-width intervals, on the other hand, were assigned probabilities that were, on the average, considerably larger than the corresponding relative frequencies. In summary, the results indicate that weather forecasters can use credible intervals to describe the uncertainty contained in their temperature forecasts. The implications of these experimental results for probability forecasting in general and temperature forecasting in particular are discussed