Ensembles used for probabilistic weather forecasting often exhibit a spread-error correlation, but they tend to be underdispersive. This paper proposes a statistical method for postprocessing ensembles based on Bayesian model averaging (BMA), which is a standard method for combining predictive distributions from different sources. The BMA predictive probability density function (PDF) of any quantity of interest is a weighted average of PDFs centered on the individual bias-corrected forecasts, where the weights are equal to posterior probabilities of the models generating the forecasts and reflect the models ’ relative contributions to predictive skill over the training period. The BMA weights can be used to assess the usefulness of ensemble members, and this can be used as a basis for selecting ensemble members; this can be useful given the cost of running large ensembles. The BMA PDF can be represented as an unweighted ensemble of any desired size, by simulating from the BMA predictive distribution. The BMA predictive variance can be decomposed into two components, one corresponding to the between-forecast variability, and the second to the within-forecast variability. Predictive PDFs or intervals based solely on the ensemble spread incorporate the first component but not the second. Thus BMA provides a theoretical explanation of the tendency of ensembles to exhibit a spread-error correlation but yet

The naive Bayes classifier has proved to be very effective on many real data applications. Its performance usually benefits from an accurate estimation of univariate conditional probabilities and from variable selection. However, although variable selection is a desirable feature, it is prone to overfitting. In this paper, we introduce a Bayesian regularization technique to select the most probable subset of variables compliant with the naive Bayes assumption. We also study the limits of Bayesian model averaging in the case of the naive Bayes assumption and introduce a new weighting scheme based on the ability of the models to conditionally compress the class labels. The weighting scheme on the models reduces to a weighting scheme on the variables, and finally results in a naive Bayes classifier with “soft variable selection”. Extensive experiments show that the compressionbased averaged classifier outperforms the Bayesian model averaging scheme.

Clark and McCracken (2008) argue that combining real-time point forecasts from VARs of output, prices and interest rates improves point forecast accuracy in the presence of uncertain model instabilities. In this paper, we generalize their approach to consider forecast density combinations and evaluations. Whereas Clark and Mc-Cracken (2008) show that the point forecast errors from particular equal-weight pairwise averages are typically comparable or better than benchmark univariate time series models, we show that neither approach produces accurate real-time forecast densities for recent US data. If greater weight is given to models that allow for the shifts in volatilities associated with the Great Moderation, predictive density accuracy improves substantially.

Trade theories covering Preferential Trade Agreements (PTAs) are as diverse as the literature in search of their empirical support. To account for the model uncertainty that surrounds the validity of the competing PTA theories, we introduce Bayesian Model Averaging (BMA) to the PTA literature. BMA minimizes the sum of Type I and Type II error, the mean squared error, and generates predictive distributions with optimal predictive performance. Once model uncertainty is addressed as part of the empirical strategy, we report clear evidence of Trade Creation, Trade Diversion, and Open Bloc effects. After controlling for natural trading partner effects, Trade Creation is weaker – except for the EU. To calculate the actual effects of PTAs on trade flows we show that the analysis must be comprehensive: it must control for Trade Creation and Diversion as well as all possible PTAs. Several prominent control variables are also shown to be robustly related to Trade Creation; they relate to factor endowments and economic policy.

Combined density nowcasts for quarterly Euro-area GDP growth are produced based on the real-time performance of component models. Components are distinguished by their use of “hard ” and “soft ” indicators. We consider the accuracy of the density nowcasts as within-quarter information on the monthly indicators accumulates. We focus on their ability to anticipate the recent recession probabilistically. We find that the relative utility of “soft ” data increased suddenly during the recession. But as this instability was hard to detect in real-time it helps, when producing nowcasts knowing only one month’s “hard ” data, to weight the different indicators equally. As more monthly “hard ” data arrive, better calibrated densities are obtained by giving a higher weight in the combination to these “hard ” indicators.

Although not widely known until much later, Al Gore received 202 more votes than George W. Bush on election day in Florida. George W. Bush is president because he overcame his election day deficit with overseas absentee ballots that arrived and were counted after election day. In the final official tally, Bush received 537 more votes than Gore. These numbers are taken from the official results released by the Florida Secretary of State's office and so do not reflect overvotes, undervotes, unsuccessful litigation, butterfly ballot problems, recounts that might have been allowed but were not, or any other hypothetical divergence between voter preferences and counted votes. After the election, The New York Times conducted a six month investigation and found that 680 of the overseas absentee ballots were illegally counted, and almost no one has publicly disagreed with their assessment. In this paper, we describe the statistical procedures we developed and implemented for the Times to ascertain whether disqualifying these 680 ballots would have changed the outcome of the election. We present a variety of new empirical results that delineate the precise conditions under which Al Gore would have been elected president, and offer new evidence of the striking effectiveness of the Republican effort to prevent local election officials from applying election law equally to all Florida citizens.

ABSTRACT: A message coming out of the recent Bayesian literature on cointegration is that it is important to elicit a prior on the space spanned by the cointegrating vectors (as opposed to a particular identified choice for these vectors). In previous work, such priors have been found to greatly complicate computation. In this paper, we develop algorithms to carry out efficient posterior simulation in cointegration models. In particular, we develop a collapsed Gibbs sampling algorithm which can be used with just-identifed models and demonstrate that it has very large computational advantages relative to existing approaches. For over-identifed models, we develop a parameter-augmented Gibbs sampling algorithm and demonstrate that it also has attractive computational properties.

A popular macroeconomic forecasting strategy takes combinations across many models to hedge against model instabilities of unknown timing; see (among others) Stock & Watson (2004), Clark & McCracken (2009), and Jore, Mitchell and Vahey (2009). The scope of such ensemble forecasting exercises usually excludes Dynamic Stochastic General Equilibrium (DSGE) models, such as those advocated by Del Negro and Schorfheide (2004) and Smets and Wouters (2007), limiting the computational burden. In this paper, we use an expert combination framework (Winkler, 1981) to combine forecast densities from Vector Autoregressions (VARs), and a DSGE model (NEMO: the Norges Bank core policymaking macromodel). We show that the predictive densities from the DSGE model are competitive with those from a VAR ensemble if the VAR components are restricted to have constant parameters. In this case, both the VAR ensemble and the DSGE forecast densities are poorly calibrated. However, a VAR ensemble which encompasses structural break components produces well-calibrated forecast densities. The VARs with breaks are

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