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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
Spline adaptation in extended linear models
 Statistical Science
, 2002
"... Abstract. In many statistical applications, nonparametric modeling can provide insight into the features of a dataset that are not obtainable by other means. One successful approach involves the use of (univariate or multivariate) spline spaces. As a class, these methods have inherited much from cla ..."
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Cited by 12 (2 self)
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Abstract. In many statistical applications, nonparametric modeling can provide insight into the features of a dataset that are not obtainable by other means. One successful approach involves the use of (univariate or multivariate) spline spaces. As a class, these methods have inherited much from classical tools for parametric modeling. For example, stepwise variable selection with spline basis terms is a simple scheme for locating knots (breakpoints) in regions where the data exhibit strong, local features. Similarly, candidate knot con gurations (generated by this or some other search technique), are routinely evaluated with traditional selection criteria like AIC or BIC. In short, strategies typically applied in parametric model selection have proved useful in constructing exible, lowdimensional models for nonparametric problems. Until recently, greedy, stepwise procedures were most frequently suggested in the literature. Researchinto Bayesian variable selection, however, has given rise to a number of new splinebased methods that primarily rely on some form of Markov chain Monte Carlo to identify promising knot locations. In this paper, we consider various alternatives to greedy, deterministic schemes, and present aBayesian framework for studying adaptation in the context of an extended linear model (ELM). Our major test cases are Logspline density estimation and (bivariate) Triogram regression models. We selected these because they illustrate a number of computational and methodological issues concerning model adaptation that arise in ELMs.
The Effect of Priors on Approximate Bayes Factors from MCMC Output.” Unpublished manuscript
"... The MCMC approach to calculating approximate Bayes factors is considered. The calculation, consisting of a loglikelihood, a prior, and a posterior, presents an excellent opportunity to observe directly the effects of priors on Bayes factors. Three empirical examples demonstrate that Bayes factors a ..."
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Cited by 1 (1 self)
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The MCMC approach to calculating approximate Bayes factors is considered. The calculation, consisting of a loglikelihood, a prior, and a posterior, presents an excellent opportunity to observe directly the effects of priors on Bayes factors. Three empirical examples demonstrate that Bayes factors are sensitive to a combination of the prior variance and the difference in the number of parameters between the rival models. a I thank Susan Murphy for helpful discussions and Paul Huth, Christopher Gelpi, D.
unknown title
, 2007
"... A temporal hidden Markov regression model for the analysis of gene regulatory networks ..."
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A temporal hidden Markov regression model for the analysis of gene regulatory networks
Bayesian estimation in Kibble’s bivariate gamma distribution
"... The paper describes Bayesian estimation for the parameters of Kibble’s (1941) bivariate gamma distribution. The density of this distribution can be written as a mixture, allowing for a simple data augmentation scheme. An MCMC algorithm is constructed to facilitate Bayesian estimation. We show that t ..."
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The paper describes Bayesian estimation for the parameters of Kibble’s (1941) bivariate gamma distribution. The density of this distribution can be written as a mixture, allowing for a simple data augmentation scheme. An MCMC algorithm is constructed to facilitate Bayesian estimation. We show that the resulting chain is geometrically ergodic and thus a regenerative sampling procedure is applicable allowing for estimation of ergodic means ’ standard errors. Bayesian hypothesis testing procedures are developed to test both the dependence hypothesis of the two variables as well as the hypothesis that their means are equal. A reversible jump MCMC algorithm is proposed to carry out this model selection problem. Real and simulated datasets are used to illustrate the proposed methodology. Key words and phrases: Downton’s bivariate exponential distribution; Kibble’s bivariate gamma distribution; Markov chain Monte Carlo; regenerative simulation; reversible jump. 1
Model Averaging in Economics: An Overview ∗ Enrique MoralBenito †
, 2010
"... Standard practice in empirical research is based on two steps: first, researchers select a model from the space of all possible models; second, they proceed as if the selected model had generated the data. Therefore, uncertainty in the model selection step is typically ignored. Alternatively, model ..."
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Standard practice in empirical research is based on two steps: first, researchers select a model from the space of all possible models; second, they proceed as if the selected model had generated the data. Therefore, uncertainty in the model selection step is typically ignored. Alternatively, model averaging accounts for this model uncertainty. In this paper, I review the literature on model averaging with special emphasis on its applications to economics. Finally, as empirical illustration, I consider model averaging to examine the deterrent effect of capital punishment across states in the US. JEL Classification: C5, K4.
A PREDICTIVE LIKELIHOOD APPROACH TO POSSIBLE ENDOGENEITY – AN APPLICATION WITH US INCOMEEDUCATION DATA: Tradeoff between Estimation Precision and the Necessity of Instruments
, 2011
"... A simple regression of earned income on years of education in order to measure the educationincome effect neglects important issues. Although higher education levels are expected to increase an individual’s earnings, the incomeeducation relationship can be subject to omitted variables such as indiv ..."
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A simple regression of earned income on years of education in order to measure the educationincome effect neglects important issues. Although higher education levels are expected to increase an individual’s earnings, the incomeeducation relationship can be subject to omitted variables such as individuals’
On the probability of a model
"... The posterior probabilities of K given models when improper priors are used depend on the proportionality constants assigned to the prior densities corresponding to each of the models. It is shown that this assignment can be done using natural geometric priors in multiple regression problems if the ..."
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The posterior probabilities of K given models when improper priors are used depend on the proportionality constants assigned to the prior densities corresponding to each of the models. It is shown that this assignment can be done using natural geometric priors in multiple regression problems if the normal distribution of the residual errors is truncated. This truncation is a realistic modification of the regression models, and since it will be made far away from the mean, it has no other effect beyond the determination of the proportionality constants, provided that the sample size is not too large. In the case K = 2, the posterior odds ratio is related to the usual F statistic in ”classical ” statistics. Assuming zeroone losses the optimal selection of a regression model is achieved by maximizing the posterior probability of a submodel. It is shown that the geometric criterion obtained in this way is asymptotically equivalent to Schwarz’s asymptotic Bayesian criterion, sometimes called the BIC criterion. An example of polynomial regression is used to provide numerical comparisons between the new geometric criterion, the BIC criterion and the Akaike information criterion.