Gail Blattenberger

Separating the Brier Score into Calibration and Refinement Components: A Graphical Exposition

Abstract Proper scoring rules of subjective probability assessments have been shown to be separable into distinct calibration and refinement components. This article presents a graphical description of this separation theorem as applied to the Brier score (quadratic loss) of assessed probabilities for a sequence of observable events. Configurations of achievable calibration, refinement, and Brier scores are exhibited in three-dimensional space and by projection into interpretable subspaces. Relationships of calibration and refinement to the usual sum-of-squares partition in analysis of variance are denoted. Controversy concerning the implications of long-run calibration for probability theory based solely on the principle of coherence is outlined.

Avalanche Forecasting: Using Bayesian Additive Regression Trees (BART)

During the ski season, professional avalanche forecasters working for the Utah Department of Transportation (UDOT) monitor one of the most dangerous highways in the world. These forecasters continually evaluate the risk of avalanche activity and make road closure decisions.

Understanding the cell phone effect on vehicle fatalities: a Bayesian view

This article examines the potential effect of various factors on motor vehicle fatality rates using a rich set of panel data and classical regression analysis combined with Bayesian Extreme Bounds Analysis (EBA), Bayesian Model Averaging (BMA) and Stochastic Search Variable Selection (SSVS) procedures. The variables examined in the models include traditional motor vehicle and socioeconomic factors. In addition, the models address the effects of cell phone usage on such accidents. The use of both classical and Bayesian techniques diminish the model and parameter uncertainties which afflict more conventional modelling methods which rely on only one of the two methods.

An Application of Operational-Subjective Statistical Methods to Rational Expectations

This article presents a sequential scoring analysis of six econometric forecast distributions for the main components of the annual U.S. gross national product (GNP) accounts—nominal GNP, real GNP, and the implicit price deflator. Analysis of sequential forecasts is presented in terms of proper scoring rules. Computations relevant to the calibration and refinement properties of the forecast distributions are discussed. Annual data are studied for the period 1952–1982. The six forecast distributions are distinguished by the different stances they entail with respect to a subjectivist characterization of the rational-expectations hypothesis.

Road Closure: Combining Data and Expert Opinion

Decisions to close the Little Cottonwood Canyon Highway to vehicular traffic are made by avalanche forecasters. These decisions are based on professional experience and on careful monitoring of the prevailing conditions. Considerable data on weather and snowpack conditions exist. These data are informally employed by the forecasters in the road closure decision but presently they do not use formal statistical methods. This paper attempts a more formal statistical analysis to determine to whether this might facilitate the road closure decision. The conclusion is that the statistical model provides information relevant to the road closure decision that is not identical to that of the experts. When the expert decision is augmented by the statistical information, better decisions are reached compared with decisions based on either the expert opinion alone or the statistical model.

Money Demand Revisited: An Operational Subjective Approach

This paper proposes a method of data analysis founded on the philosophy and understanding of uncertain knowledge developed by Bruno de Finetti. Specifically, the paper investigates the informational content of interest rates for the prediction of M1. This empirical application replicates that of Cooley and Leroy (1981) and McAleer, Pagan, and Volker (1985), but the procedures and their interpretation follow the operational subjective approach. The issue of an autocorrelated error structure is recast in the operational subjective context. Methods are developed to assess the interest sensitivity of the demand for money in this context. Copyright 1996 by John Wiley & Sons, Ltd.

Variable Selection in Bayesian Models: Using Parameter Estimation and Non Parameter Estimation Methods

Abstract This paper examines variable selection among various factors related to motor vehicle fatality rates using a rich set of panel data. Four Bayesian methods are used. These include Extreme Bounds Analysis (EBA), Stochastic Search Variable Selection (SSVS), Bayesian Model Averaging (BMA), and Bayesian Additive Regression Trees (BART). The first three of these employ parameter estimation, the last, BART, involves no parameter estimation. Nonetheless, it also has implications for variable selection. The variables examined in the models include traditional motor vehicle and socioeconomic factors along with important policy-related variables. Policy recommendations are suggested with respect to cell phone use, modernization of the fleet, alcohol use, and diminishing suicidal behavior.