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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 127 (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 16 (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 2 (2 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.
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.
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"... The stopsignal paradigm is frequently used to study response inhibition. In this paradigm, participants perform a twochoice response time task where the primary task is occasionally interrupted by a stopsignal that prompts participants to withhold their response. The primary goal is to estimate t ..."
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The stopsignal paradigm is frequently used to study response inhibition. In this paradigm, participants perform a twochoice response time task where the primary task is occasionally interrupted by a stopsignal that prompts participants to withhold their response. The primary goal is to estimate the latency of the unobservable stop response (stop signal reaction time or SSRT). Recently, Matzke, Dolan, Logan, Brown, and Wagenmakers (in press) have developed a Bayesian parametric approach that allows for the estimation of the entire distribution of SSRTs. The Bayesian parametric approach assumes that SSRTs are exGaussian distributed and uses Markov chain Monte Carlo sampling to estimate the parameters of the SSRT distribution. Here we present an efficient and userfriendly software implementation of the Bayesian parametric approach —BEESTS — that can be applied to individual as well as hierarchical stopsignal data. BEESTS comes with an easytouse graphical user interface and provides users with summary statistics of the posterior distribution of the parameters as well various diagnostic tools to assess the quality of the parameter estimates. The software is open source and runs on Windows and OS X operating systems. In sum, BEESTS allows experimental and clinical psychologists to estimate entire distributions of SSRTs and hence facilitates the more rigorous analysis of stopsignal data.
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.
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"... doi:10.1093/biostatistics/kxm007 A temporal hidden Markov regression model for the analysis of gene regulatory networks ..."
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doi:10.1093/biostatistics/kxm007 A temporal hidden Markov regression model for the analysis of gene regulatory networks
lu h
, 2005
"... We analyzed the phylogeny of the Neotropical pitvipers within the Porthidium group (including intraspeciWc through intergeneric relationships) using 1.4 kb of DNA sequences from two mitochondrial proteincoding genes (ND4 and cytb). We investigated how Bayesian Markov chain MonteCarlo (MCMC) ph ..."
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We analyzed the phylogeny of the Neotropical pitvipers within the Porthidium group (including intraspeciWc through intergeneric relationships) using 1.4 kb of DNA sequences from two mitochondrial proteincoding genes (ND4 and cytb). We investigated how Bayesian Markov chain MonteCarlo (MCMC) phylogenetic hypotheses based on this ‘mesoscale ’ dataset were aVected by analysis under various complex models of nucleotide evolution that partition models across the dataset. We develop an approach, employing three statistics (Akaike weights, Bayes factors, and relative Bayes factors), for examining the performance of complex models in order to identify the bestWt model for data analysis. Our results suggest that: (1) model choice may have important practical eVects on phylogenetic conclusions even for mesoscale datasets, (2) the use of a complex partitioned model did not produce widespread increases or decreases in nodal posterior probability support, and (3) most diVerences in resolution resulting from model choice were concentrated at deeper nodes. Our phylogenetic estimates of relationships among members of the Porthidium group (genera: Atropoides, Cerrophidion, and Porthidium) resolve the monophyly of the three genera. Bayesian MCMC results suggest that Cerrophidion and Porthidium form a clade that is the sister taxon to Atropoides. In addition to resolving the intraspeciWc relationships among a majority of Porthidium group taxa, our results highlight phylogeographic patterns across Middle and South America and suggest that each of the three genera may harbor undescribed species diversity.