Abstract: Bayesian inference in a time series model provides exact, out-of-sample predictive distributions that fully and coherently incorporate parameter uncertainty. This study compares and evaluates Bayesian predictive distributions from alternative models, using as an illustration five alternative models of asset returns applied to daily S&P 500 returns from 1972 through 2005. The comparison exercise uses predictive likelihoods and is inherently Bayesian. The evaluation exercise uses the probability integral transform and is inherently frequentist. The illustration shows that the two approaches can be complementary, each identifying strengths and weaknesses in models that are not evident using the other. JEL classification: C11, C53 Key words: forecasting, GARCH, inverse probability transform, Markov-mixture, predictive likelihood, S&P 500 returns, stochastic volatility The authors gratefully acknowledge financial support from NSF grant SBR-0720547. The views expressed here are the authors ’ and not necessarily those of the Federal Reserve Bank of Atlanta or the Federal Reserve System. Any remaining errors are the authors ’ responsibility.

the Joint Ensemble Forecasting System (JEFS) under subcontract S06-47225 from the University

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The technology to harvest electricity from wind energy is now advanced enough to make entire cities powered by it a reality. High-quality short-term forecasts of wind speed are vital to making this a more reliable energy source. Gneiting et al. (2006) have introduced a model for the average wind speed two hours ahead based on both spatial and temporal information. The forecasts produced by this model are accurate, and subject to accuracy, the predictive distribution is sharp, i.e., highly concentrated around its center. However, this model is split into nonunique regimes based on the wind direction at an off-site location. This paper both generalizes and improves upon this model by treating wind direction as a circular variable and including it in the model. It is robust in many experiments, such as predicting at new locations. We compare this with the more common approach of modeling wind speeds and directions in the Cartesian space and use a skew-t distribution for the errors. The quality of the predictions from all of these models can be more realistically assessed with a loss measure that depends upon the power curve relating wind speed to power output. This proposed loss measure yields more insight into the true value of each model’s predictions. Some key words: Circular variable, power curve, skew-t distribution, wind direction, wind speed.

Abstract. A potential downside of prediction markets is that they may incentivize agents to take undesirable actions in the real world. For example, a prediction market for whether a terrorist attack will happen may incentivize terrorism, and an in-house prediction market for whether a product will be successfully released may incentivize sabotage. In this paper, we study principal-aligned prediction mechanisms– mechanisms that do not incentivize undesirable actions. We characterize all principal-aligned proper scoring rules, and we show an “overpayment” result, which roughly states that with n agents, any prediction mechanism that is principal-aligned will, in the worst case, require the principal to pay Θ(n) times as much as a mechanism that is not. We extend our model to allow uncertainties about the principal’s utility and restrictions on agents ’ actions, showing a richer characterization and a similar “overpayment ” result.

Summary. We discuss tools for the evaluation of probabilistic forecasts and the critique of statistical models for ordered discrete data. Our proposals include a non-randomized version of the probability integral transform, marginal calibration diagrams and proper scoring rules, such as the predictive deviance. In case studies, we critique count regression models for patent data, and assess the predictive performance of Bayesian age-period-cohort models for larynx cancer counts in Germany.

Sloughter for sharing their insights and providing data. This research was sponsored by the National Science Foundation under Joint Ensemble Forecasting System (JEFS) subaward No. S06-47225 with the University Corporation for Atmospheric Research (UCAR), as well as grants No. ATM-0724721 and No. DMS-0706745. Bayesian model averaging (BMA) is a statistical postprocessing technique that generates calibrated and sharp predictive probability density functions (PDFs) from forecast ensembles. It represents the predictive PDF as a weighted average of PDFs centered on the bias-corrected ensemble members, where the weights reflect the relative skill of the individual members over a training period. This work adapts the BMA approach to situations that arise frequently in practice, namely, when one or more of the member forecasts are exchangeable, and when there are missing ensemble members. Exchangeable members differ in random perturbations only, such as the members of bred ensembles, singular vector ensembles, or ensemble Kalman filter systems. Accounting for exchangeability simplifies the BMA approach, in that the BMA weights and the parameters of the component PDFs can be assumed to

We unify f-divergences, Bregman divergences, surrogate regret bounds, proper scoring rules, cost curves, ROC-curves and statistical information. We do this by systematically studying integral and variational representations of these various objects and in so doing identify their primitives which all are related to cost-sensitive binary classification. As well as developing relationships between generative and discriminative views of learning, the new machinery leads to tight and more general surrogate regret bounds and generalised Pinsker inequalities relating f-divergences to variational divergence. The new viewpoint also illuminates existing algorithms: it provides a new derivation of Support Vector Machines in terms of divergences and relates Maximum Mean Discrepancy to Fisher Linear Discriminants.

A graphical multiagent model (GMM) represents a joint distribution over the behavior of a set of agents. One source of knowledge about agents ' behavior may come from gametheoretic analysis, as captured by several graphical game representations developed in recent years. GMMs generalize this approach to express arbitrary distributions, based on game descriptions or other sources of knowledge bearing on beliefs about agent behavior. To illustrate the exibility of GMMs, we exhibit game-derived models that allow probabilistic deviation from equilibrium, as well as models based on heuristic action choice. We investigate three di erent methods of integrating these models into a single model representing the combined knowledge sources. To evaluate the predictive performance of the combined model, we treat as actual outcome the behavior produced by a reinforcement learning process. We nd that combining the two knowledge sources, using any of the methods, provides better predictions than either source alone. Among the combination methods, mixing data outperforms the opinion pool and direct update methods investigated in this empirical trial. 1

This work is motivated by a mobility study conducted in the city of Munich, Germany. The variable of interest is a binary response, which indicates whether public transport has been utilized or not. One of the central questions is to identify areas of low/high utilization of public transport after adjusting for explanatory factors such as trip, individual and household attributes. For the spatial effects a modification of a class of Markov Random Fields (MRF) models with proper joint distributions introduced by Pettitt et al. (2002) is developed. It contains the intrinsic MRF in the limit and allows for efficient Markov Chain Monte Carlo (MCMC) algorithms. Further cluster effects using group and individual approaches are taken into consideration. The first one models heterogeneity between clusters, while the second one models heterogeneity within clusters. A naive approach to include individual cluster effects results in an unidentifiable model. It is shown how a re-parametrization gives identifiable parameters. This provides a new approach for modeling heterogeneity within clusters. Finally the proposed model classes are applied to the mobility study. Key words: binary regression, spatial effects, group and individual cluster effects, MCMC, transport mode decisions