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77
Bayesian Model Averaging for Linear Regression Models
 Journal of the American Statistical Association
, 1997
"... We consider the problem of accounting for model uncertainty in linear regression models. Conditioning on a single selected model ignores model uncertainty, and thus leads to the underestimation of uncertainty when making inferences about quantities of interest. A Bayesian solution to this problem in ..."
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Cited by 185 (13 self)
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We consider the problem of accounting for model uncertainty in linear regression models. Conditioning on a single selected model ignores model uncertainty, and thus leads to the underestimation of uncertainty when making inferences about quantities of interest. A Bayesian solution to this problem involves averaging over all possible models (i.e., combinations of predictors) when making inferences about quantities of
Assessment and Propagation of Model Uncertainty
, 1995
"... this paper I discuss a Bayesian approach to solving this problem that has long been available in principle but is only now becoming routinely feasible, by virtue of recent computational advances, and examine its implementation in examples that involve forecasting the price of oil and estimating the ..."
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Cited by 108 (0 self)
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this paper I discuss a Bayesian approach to solving this problem that has long been available in principle but is only now becoming routinely feasible, by virtue of recent computational advances, and examine its implementation in examples that involve forecasting the price of oil and estimating the chance of catastrophic failure of the U.S. Space Shuttle.
Using Bayesian model averaging to calibrate forecast ensembles. Monthly Weather Review 133
, 2005
"... Ensembles used for probabilistic weather forecasting often exhibit a spreaderror 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 distr ..."
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Cited by 71 (28 self)
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Ensembles used for probabilistic weather forecasting often exhibit a spreaderror 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 biascorrected 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 betweenforecast variability, and the second to the withinforecast 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 spreaderror correlation but yet
Understanding Trend and Cycle in Asset Values: Reevaluating the Wealth Effect on Consumption
 American Economic Review
, 2004
"... Both textbook economics and common sense teach us that the value of household wealth should be related to consumer spending. Early academic work by Franco Modigliani (1971) suggested that a dollar increase in wealth (holding � xed labor income) leads to an increase in consumer spending of about � ve ..."
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Cited by 60 (4 self)
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Both textbook economics and common sense teach us that the value of household wealth should be related to consumer spending. Early academic work by Franco Modigliani (1971) suggested that a dollar increase in wealth (holding � xed labor income) leads to an increase in consumer spending of about � ve cents. Since then, the socalled “wealth effect ” on consumption has increasingly crept into both mainstream and policy discussions of the macroeconomy. 1 Today, it is commonly presumed that signi �cant movements in wealth will be associated with movements in consumer spending, either contemporaneously or subsequently. Quantitative estimates of roughly the magnitude reported by Modigliani are routinely cited in
Forecast Combinations
 Handbook of Economic Forecasting
, 2006
"... Forecast combinations have frequently been found in empirical studies to produce better forecasts on average than methods based on the exante best individual forecasting model. Moreover, simple combinations that ignore correlations between forecast errors often dominate more refined combination sch ..."
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Cited by 49 (2 self)
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Forecast combinations have frequently been found in empirical studies to produce better forecasts on average than methods based on the exante best individual forecasting model. Moreover, simple combinations that ignore correlations between forecast errors often dominate more refined combination schemes aimed at estimating the theoretically optimal combination weights. In this chapter we analyze theoretically the factors that determine the advantages from combining forecasts (for example, the degree of correlation between forecast errors and the relative size of the individual models’ forecast error variances). Although the reasons for the success of simple combination schemes are poorly understood, we discuss several possibilities related to model misspecification, instability (nonstationarities) and estimation error in situations where thenumbersofmodelsislargerelativetothe available sample size. We discuss the role of combinations under asymmetric loss and consider combinations of point, interval and probability forecasts. Key words: Forecast combinations; pooling and trimming; shrinkage methods; model misspecification, diversification gains
Model Selection and Accounting for Model Uncertainty in Linear Regression Models
, 1993
"... We consider the problems of variable selection and accounting for model uncertainty in linear regression models. Conditioning on a single selected model ignores model uncertainty, and thus leads to the underestimation of uncertainty when making inferences about quantities of interest. The complete B ..."
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Cited by 47 (6 self)
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We consider the problems of variable selection and accounting for model uncertainty in linear regression models. Conditioning on a single selected model ignores model uncertainty, and thus leads to the underestimation of uncertainty when making inferences about quantities of interest. The complete Bayesian solution to this problem involves averaging over all possible models when making inferences about quantities of interest. This approach is often not practical. In this paper we offer two alternative approaches. First we describe a Bayesian model selection algorithm called "Occam's "Window" which involves averaging over a reduced set of models. Second, we describe a Markov chain Monte Carlo approach which directly approximates the exact solution. Both these model averaging procedures provide better predictive performance than any single model which might reasonably have been selected. In the extreme case where there are many candidate predictors but there is no relationship between any of them and the response, standard variable selection procedures often choose some subset of variables that yields a high R² and a highly significant overall F value. We refer to this unfortunate phenomenon as "Freedman's Paradox" (Freedman, 1983). In this situation, Occam's vVindow usually indicates the null model as the only one to be considered, or else a small number of models including the null model, thus largely resolving the paradox.
The incidental parameter problem since 1948
 JOURNAL OF ECONOMETRICS 95 (2000) 391413
, 2000
"... This paper was written to mark the 50th anniversary of Neyman and Scott's Econometrica paper defining the incidental parameter problem. It surveys the history both of the paper and of the problem in the statistics and econometrics literature. ..."
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Cited by 46 (0 self)
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This paper was written to mark the 50th anniversary of Neyman and Scott's Econometrica paper defining the incidental parameter problem. It surveys the history both of the paper and of the problem in the statistics and econometrics literature.
Probabilistic quantitative precipitation forecasting using Bayesian model averaging. Monthly Weather Review 135
 Monthly Weather Review
, 2007
"... and useful comments, and for providing data. They are also grateful to Patrick Tewson for implementing the UW Ensemble BMA website. This research was supported by the DoD Multidisciplinary University Research Initiative (MURI) program administered by the Office of Naval Research under Grant N000140 ..."
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Cited by 32 (20 self)
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and useful comments, and for providing data. They are also grateful to Patrick Tewson for implementing the UW Ensemble BMA website. This research was supported by the DoD Multidisciplinary University Research Initiative (MURI) program administered by the Office of Naval Research under Grant N000140110745. Bayesian model averaging (BMA) is a statistical way of postprocessing forecast ensembles to create predictive probability density functions (PDFs) for weather quantities. It represents the predictive PDF as a weighted average of PDFs centered on the individual biascorrected forecasts, where the weights are posterior probabilities of the models generating the forecasts and reflect the forecasts ’ relative contributions to predictive skill over a training period. It was developed initially for quantities whose PDFs can be approximated by normal distributions, such as temperature and sealevel pressure. BMA does not apply in its original form to precipitation, because the predictive PDF of precipitation is nonnormal in two major ways: it has a positive probability of being equal to zero, and it is skewed. Here we extend BMA to probabilistic quantitative precipitation forecasting. The predictive PDF corresponding to
2003), “Policy Evaluation in Uncertain Economic Environments (with discussion
 Brookings Papers on Economic Activity
"... It will be remembered that the seventy translators of the Septuagint were shut up in seventy separate rooms with the Hebrew text and brought out with them, when they emerged, seventy identical translations. Would the same miracle be vouchsafed if seventy multiple correlators were shut up with the sa ..."
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Cited by 31 (5 self)
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It will be remembered that the seventy translators of the Septuagint were shut up in seventy separate rooms with the Hebrew text and brought out with them, when they emerged, seventy identical translations. Would the same miracle be vouchsafed if seventy multiple correlators were shut up with the same statistical material? And anyhow, I suppose, if each had a different economist perched on his a priori, that would make a difference to the outcome. 1 This paper describes some approaches to macroeconomic policy evaluation in the presence of uncertainty about the structure of the economic environment under study. The perspective we discuss is designed to facilitate policy evaluation for several forms of uncertainty. For example, our approach may be used when an analyst is unsure about the appropriate economic theory that should be assumed to apply, or about the particular functional forms that translate a general theory into a form amenable to statistical analysis. As such, the methods we describe are, we believe, particularly useful in a range of macroeconomic contexts where fundamental disagreements exist as to the determinants of the problem under study. In addition, this approach recognizes that even if economists agree on the
Dangers of DataDriven Inference: The Case of Calendar Effects in Stock Returns
 Journal of Finance
, 1998
"... Economics is primarily a nonexperimental science. Typically, we cannot generate new data sets on which to test hypotheses independently of the data that may have led to a particular theory. The common practice of using the same data set to formulate and test hypotheses introduces datasnooping bias ..."
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Cited by 26 (3 self)
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Economics is primarily a nonexperimental science. Typically, we cannot generate new data sets on which to test hypotheses independently of the data that may have led to a particular theory. The common practice of using the same data set to formulate and test hypotheses introduces datasnooping biases that, if not accounted for, invalidate the assumptions underlying classical statistical inference. A striking example of a datadriven discovery is the presence of calendar effects in stock returns. There appears to be very substantial evidence of systematic abnormal stock returns related to the day of the week, the week of the month, the month of the year, the turn of the month, holidays, and so forth. However, this evidence has largely been considered without accounting for the intensive search preceding it. In this paper we use 100 years of daily data and a new bootstrap procedure that allows us to explicitly measure the distortions in statistical inference induced by datasnooping. We find that although nominal Pvalues of individual calendar rules are extremely significant, once evaluated in the context of the full universe from which such rules were drawn, calendar effects no longer remain significant.