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173
Bayes Factors
, 1995
"... In a 1935 paper, and in his book Theory of Probability, Jeffreys developed a methodology for quantifying the evidence in favor of a scientific theory. The centerpiece was a number, now called the Bayes factor, which is the posterior odds of the null hypothesis when the prior probability on the null ..."
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Cited by 981 (70 self)
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In a 1935 paper, and in his book Theory of Probability, Jeffreys developed a methodology for quantifying the evidence in favor of a scientific theory. The centerpiece was a number, now called the Bayes factor, which is the posterior odds of the null hypothesis when the prior probability on the null is onehalf. Although there has been much discussion of Bayesian hypothesis testing in the context of criticism of P values, less attention has been given to the Bayes factor as a practical tool of applied statistics. In this paper we review and discuss the uses of Bayes factors in the context of five scientific applications in genetics, sports, ecology, sociology and psychology.
Investing for the long run when returns are predictable
 Journal of Finance
, 2000
"... We examine how the evidence of predictability in asset returns affects optimal portfolio choice for investors with long horizons. Particular attention is paid to estimation risk, or uncertainty about the true values of model parameters. We find that even after incorporating parameter uncertainty, th ..."
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Cited by 283 (0 self)
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We examine how the evidence of predictability in asset returns affects optimal portfolio choice for investors with long horizons. Particular attention is paid to estimation risk, or uncertainty about the true values of model parameters. We find that even after incorporating parameter uncertainty, there is enough predictability in returns to make investors allocate substantially more to stocks, the longer their horizon. Moreover, the weak statistical significance of the evidence for predictability makes it important to take estimation risk into account; a longhorizon investor who ignores it may overallocate to stocks by a sizeable amount. ONE OF THE MORE STRIKING EMPIRICAL FINDINGS in recent financial research is the evidence of predictability in asset returns. 1 In this paper we examine the implications of this predictability for an investor seeking to make sensible portfolio allocation decisions. We approach this question from the perspective of horizon effects: Given the evidence of predictability in returns, should a longhorizon investor allocate his wealth differently from a shorthorizon investor? The motivation for thinking about the problem in these terms is the classic work of Samuelson ~1969! and Merton ~1969!. They show that if asset returns are i.i.d., an investor with power utility who rebalances his portfolio optimally should choose the same asset allocation, regardless of investment horizon. In light of the growing body of evidence that returns are predictable, the investor’s horizon may no longer be irrelevant. The extent to which the horizon does play a role serves as an interesting and convenient way of thinking about how predictability affects portfolio choice. Moreover, the results may shed light on the common but controversial advice that investors with long horizons should allocate more heavily to stocks. 2
Using simulation methods for Bayesian econometric models: Inference, development and communication
 Econometric Review
, 1999
"... This paper surveys the fundamental principles of subjective Bayesian inference in econometrics and the implementation of those principles using posterior simulation methods. The emphasis is on the combination of models and the development of predictive distributions. Moving beyond conditioning on a ..."
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Cited by 199 (15 self)
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This paper surveys the fundamental principles of subjective Bayesian inference in econometrics and the implementation of those principles using posterior simulation methods. The emphasis is on the combination of models and the development of predictive distributions. Moving beyond conditioning on a fixed number of completely specified models, the paper introduces subjective Bayesian tools for formal comparison of these models with as yet incompletely specified models. The paper then shows how posterior simulators can facilitate communication between investigators (for example, econometricians) on the one hand and remote clients (for example, decision makers) on the other, enabling clients to vary the prior distributions and functions of interest employed by investigators. A theme of the paper is the practicality of subjective Bayesian methods. To this end, the paper describes publicly available software for Bayesian inference, model development, and communication and provides illustrations using two simple econometric models. *This paper was originally prepared for the Australasian meetings of the Econometric Society in Melbourne, Australia,
Sparse graphical models for exploring gene expression data
 Journal of Multivariate Analysis
, 2004
"... DMS0112069. Any opinions, findings, and conclusions or recommendations expressed in this material are ..."
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Cited by 132 (22 self)
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DMS0112069. Any opinions, findings, and conclusions or recommendations expressed in this material are
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.
Stock Return Predictability and Model Uncertainty
, 2002
"... We use Bayesian model averaging to analyze the sample evidence on return predictability in the presence of model uncertainty. The analysis reveals insample and outofsample predictability, and shows that the outofsample performance of the Bayesian approach is superior to that of model selecti ..."
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Cited by 98 (3 self)
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We use Bayesian model averaging to analyze the sample evidence on return predictability in the presence of model uncertainty. The analysis reveals insample and outofsample predictability, and shows that the outofsample performance of the Bayesian approach is superior to that of model selection criteria. We find that term and market premia are robust predictors. Moreover, smallcap value stocks appear more predictable than largecap growth stocks. We also investigate the implications of model uncertainty from investment management perspectives. We show that model uncertainty is more important than estimation risk, and investors who discard model uncertainty face large utility losses.
Approximate Bayes Factors and Accounting for Model Uncertainty in Generalized Linear Models
, 1993
"... Ways of obtaining approximate Bayes factors for generalized linear models are described, based on the Laplace method for integrals. I propose a new approximation which uses only the output of standard computer programs such as GUM; this appears to be quite accurate. A reference set of proper priors ..."
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Cited by 96 (28 self)
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Ways of obtaining approximate Bayes factors for generalized linear models are described, based on the Laplace method for integrals. I propose a new approximation which uses only the output of standard computer programs such as GUM; this appears to be quite accurate. A reference set of proper priors is suggested, both to represent the situation where there is not much prior information, and to assess the sensitivity of the results to the prior distribution. The methods can be used when the dispersion parameter is unknown, when there is overdispersion, to compare link functions, and to compare error distributions and variance functions. The methods can be used to implement the Bayesian approach to accounting for model uncertainty. I describe an application to inference about relative risks in the presence of control factors where model uncertainty is large and important. Software to implement the
Bayes factors and model uncertainty
 DEPARTMENT OF STATISTICS, UNIVERSITY OFWASHINGTON
, 1993
"... In a 1935 paper, and in his book Theory of Probability, Jeffreys developed a methodology for quantifying the evidence in favor of a scientific theory. The centerpiece was a number, now called the Bayes factor, which is the posterior odds of the null hypothesis when the prior probability on the null ..."
Abstract

Cited by 89 (6 self)
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In a 1935 paper, and in his book Theory of Probability, Jeffreys developed a methodology for quantifying the evidence in favor of a scientific theory. The centerpiece was a number, now called the Bayes factor, which is the posterior odds of the null hypothesis when the prior probability on the null is onehalf. Although there has been much discussion of Bayesian hypothesis testing in the context of criticism of Pvalues, less attention has been given to the Bayes factor as a practical tool of applied statistics. In this paper we review and discuss the uses of Bayes factors in the context of five scientific applications. The points we emphasize are: from Jeffreys's Bayesian point of view, the purpose of hypothesis testing is to evaluate the evidence in favor of a scientific theory; Bayes factors offer a way of evaluating evidence in favor ofa null hypothesis; Bayes factors provide a way of incorporating external information into the evaluation of evidence about a hypothesis; Bayes factors are very general, and do not require alternative models to be nested; several techniques are available for computing Bayes factors, including asymptotic approximations which are easy to compute using the output from standard packages that maximize likelihoods; in "nonstandard " statistical models that do not satisfy common regularity conditions, it can be technically simpler to calculate Bayes factors than to derive nonBayesian significance
Bayesian Treatment of the Independent Studentt Linear Model
 JOURNAL OF APPLIED ECONOMETRICS
, 1993
"... This article takes up methods for Bayesian inference in a linear model in which the disturbances are independent and have identical Studentt distributions. It exploits the equivalence of the Studentt distribution and an appropriate scale mixture of normals, and uses a Gibbs sampler to perform the ..."
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Cited by 74 (2 self)
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This article takes up methods for Bayesian inference in a linear model in which the disturbances are independent and have identical Studentt distributions. It exploits the equivalence of the Studentt distribution and an appropriate scale mixture of normals, and uses a Gibbs sampler to perform the computations. The new method is applied to some wellknown macroeconomic time series. It is found that posterior odds ratios favor the independent Studentt linear model over the normal linear model, and that the posterior odds ratio in favor of difference stationarity over trend stationarity is often substantially less in the favored Studentt models.
Comparing asset pricing models: An investment perspective
 Journal of Financial Economics
, 2000
"... We investigate the portfolio choices of meanvarianceoptimizing investors who use sample evidence to update prior beliefs centered on either riskbased or characteristicbased pricing models. With dogmatic beliefs in such models and an unconstrained ratio of position size to capital, optimal portfo ..."
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Cited by 74 (12 self)
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We investigate the portfolio choices of meanvarianceoptimizing investors who use sample evidence to update prior beliefs centered on either riskbased or characteristicbased pricing models. With dogmatic beliefs in such models and an unconstrained ratio of position size to capital, optimal portfolios can differ across models to economically significant degrees. The differences are substantially reduced by modest uncertainty about the models ’ pricing abilities. When the ratio of position size to capital is subject to realistic constraints, the differences in portfolios across models become even less important, nonexistent in some cases.