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17
Estimating the integrated likelihood via posterior simulation using the harmonic mean identity
 Bayesian Statistics
, 2007
"... The integrated likelihood (also called the marginal likelihood or the normalizing constant) is a central quantity in Bayesian model selection and model averaging. It is defined as the integral over the parameter space of the likelihood times the prior density. The Bayes factor for model comparison a ..."
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Cited by 37 (2 self)
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The integrated likelihood (also called the marginal likelihood or the normalizing constant) is a central quantity in Bayesian model selection and model averaging. It is defined as the integral over the parameter space of the likelihood times the prior density. The Bayes factor for model comparison and Bayesian testing is a ratio of integrated likelihoods, and the model weights in Bayesian model averaging are proportional to the integrated likelihoods. We consider the estimation of the integrated likelihood from posterior simulation output, aiming at a generic method that uses only the likelihoods from the posterior simulation iterations. The key is the harmonic mean identity, which says that the reciprocal of the integrated likelihood is equal to the posterior harmonic mean of the likelihood. The simplest estimator based on the identity is thus the harmonic mean of the likelihoods. While this is an unbiased and simulationconsistent estimator, its reciprocal can have infinite variance and so it is unstable in general. We describe two methods for stabilizing the harmonic mean estimator. In the first one, the parameter space is reduced in such a way that the modified estimator involves a harmonic mean of heaviertailed densities, thus resulting in a finite variance estimator. The resulting
Bayesian finite mixtures with an unknown number of components: the allocation sampler
 University of Glasgow
, 2005
"... A new Markov chain Monte Carlo method for the Bayesian analysis of finite mixture distributions with an unknown number of components is presented. The sampler is characterized by a state space consisting only of the number of components and the latent allocation variables. Its main advantage is that ..."
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Cited by 16 (1 self)
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A new Markov chain Monte Carlo method for the Bayesian analysis of finite mixture distributions with an unknown number of components is presented. The sampler is characterized by a state space consisting only of the number of components and the latent allocation variables. Its main advantage is that it can be used, with minimal changes, for mixtures of components from any parametric family, under the assumption that the component parameters can be integrated out of the model analytically. Artificial and real data sets are used to illustrate the method and mixtures of univariate and of multivariate normals are explicitly considered. The problem of label switching, when parameter inference is of interest, is addressed in a postprocessing stage.
Bayesian Inference on Mixtures of Distributions
, 2008
"... This survey covers stateoftheart Bayesian techniques for the estimation of mixtures. It complements the earlier Marin et al. (2005) by studying new types of distributions, the multinomial, latent class and t distributions. It also exhibits closed form solutions for Bayesian inference in some disc ..."
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Cited by 7 (6 self)
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This survey covers stateoftheart Bayesian techniques for the estimation of mixtures. It complements the earlier Marin et al. (2005) by studying new types of distributions, the multinomial, latent class and t distributions. It also exhibits closed form solutions for Bayesian inference in some discrete setups. At last, it sheds a new light on the computation of Bayes factors via the approximation of Chib (1995).
Performance of Bayesian model selection criteria for Gaussian mixture models. In: Frontiers of Statistical Decision Making and Bayesian
, 2010
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Modelbased Clustering of nonGaussian Panel Data
"... In this paper we propose a modelbased method to cluster units within a panel. The underlying model is autoregressive and nonGaussian, allowing for both skewness and fat tails, and the units are clustered according to their dynamic behaviour and equilibrium level. Inference is addressed from a Baye ..."
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Cited by 5 (1 self)
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In this paper we propose a modelbased method to cluster units within a panel. The underlying model is autoregressive and nonGaussian, allowing for both skewness and fat tails, and the units are clustered according to their dynamic behaviour and equilibrium level. Inference is addressed from a Bayesian perspective and model comparison is conducted using the formal tool of Bayes factors. Particular attention is paid to prior elicitation and posterior propriety. We suggest priors that require little subjective input from the user and possess hierarchical structures that enhance the robustness of the inference. Two examples illustrate the methodology: one analyses economic growth of OECD countries and the second one investigates employment growth of Spanish manufacturing firms.
Estimating and projecting trends in HIV/AIDS generalized epidemics using incremental mixture importance sampling. Biometrics 66(4
, 2010
"... The Joint United Nations Programme on HIV/AIDS (UNAIDS) has decided to use Bayesian melding as the basis for its probabilistic projections of HIV prevalence in countries with generalized epidemics. This combines a mechanistic epidemiological model, prevalence data and expert opinion. Initially, the ..."
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Cited by 4 (2 self)
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The Joint United Nations Programme on HIV/AIDS (UNAIDS) has decided to use Bayesian melding as the basis for its probabilistic projections of HIV prevalence in countries with generalized epidemics. This combines a mechanistic epidemiological model, prevalence data and expert opinion. Initially, the posterior distribution was approximated by samplingimportanceresampling, which is simple to implement, easy to interpret, transparent to users and gave acceptable results for most countries. For some countries, however, this is not computationally efficient because the posterior distribution tends to be concentrated around nonlinear ridges and can also be multimodal. We propose instead Incremental Mixture Importance Sampling (IMIS), which iteratively builds up a better importance sampling function. This retains the simplicity and transparency of sampling importance resampling, but is much more efficient computationally. It also leads to a simple estimator of the integrated likelihood that is the basis for Bayesian model comparison and model averaging. In simulation experiments and on real data it outperformed both sampling importance resampling and three publicly available generic Markov chain Monte Carlo algorithms for this
Variable selection in regression mixture modeling for the discovery of gene regulatory networks
 Journal of the American Statistical Association
, 2007
"... The profusion of genomic data through genome sequencing and gene expression microarray technology has facilitated statistical research in determining gene interactions regulating a biological process. Current methods generally consist of a twostage procedure: clustering gene expression measurement ..."
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Cited by 2 (0 self)
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The profusion of genomic data through genome sequencing and gene expression microarray technology has facilitated statistical research in determining gene interactions regulating a biological process. Current methods generally consist of a twostage procedure: clustering gene expression measurements, and searching for regulatory “switches”, typically short, conserved sequence patterns (motifs) in the DNA sequence adjacent to the genes. This process often leads to misleading conclusions as incorrect cluster selection may lead to missing important regulatory motifs or making many false discoveries. Treating cluster memberships as known, rather than estimated, introduces bias into analyses, preventing uncertainty about cluster parameters. Further, there is underutilization of the available data, as the sequence information is ignored for purposes of expression clustering and viceversa. We propose a way to address these issues by combining gene clustering and motif discovery in a unified framework, a mixture of hierarchical regression models, with unknown components representing the latent gene clusters, and genomic sequence features linked to the resultant gene ex
Estimates of AgeSpecific Reductions in HIV Prevalence in Uganda: Bayesian Melding Estimation and Probabilistic Population Forecast with an HIVenabled Cohort Component Projection Model
, 2010
"... We estimate agespecific HIV incidence and prevalence in Tanzania and Uganda in the late 1990s and forecast forward assuming no change in incidence. Comparisons between our forecasts of HIV prevalence and direct measures from the HIV/AIDS Indicator and Demographic and Health Surveys in the mid2000s ..."
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Cited by 2 (1 self)
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We estimate agespecific HIV incidence and prevalence in Tanzania and Uganda in the late 1990s and forecast forward assuming no change in incidence. Comparisons between our forecasts of HIV prevalence and direct measures from the HIV/AIDS Indicator and Demographic and Health Surveys in the mid2000s provide an agespecific measure of changes in HIV prevalence. In Tanzania our forecast accurately predicts agespecific HIV prevalence, suggesting little change in HIV incidence in Tanzania over the intervening decade. In Uganda our forecasts significantly overstate HIV prevalence. The age pattern of our forecast errors reflects the agespecific reductions in HIV prevalence and incidence in Uganda. Our estimates and forecasts are produced using an HIVenabled cohort component model of population projection first proposed by Heuveline (2003). We refine that model (Thomas and Clark, 2008) and implement the Bayesian melding with IMIS estimation method (Raftery and Bao, 2010). This method allows us to estimate the parameters of the Heuveline model with robust measures of uncertainty and to quantify uncertainty in the model outputs, e.g. forecasts. We validate
The AgePattern of Increases in Mortality Affected by HIV: Bayesian Fit of the HeligmanPollard Model to Data from the Agincourt HDSS Field Site in Rural Northeast South Africa
, 2010
"... A bst ract We describe the evolving agepattern of mortality in a rural population living in northeast South Africa during the growth of the HIV epidemic, 19942007. The likely effect of HIV on mortality is enormous. The probability of dying for young children and adults has risen twotofour fold, ..."
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A bst ract We describe the evolving agepattern of mortality in a rural population living in northeast South Africa during the growth of the HIV epidemic, 19942007. The likely effect of HIV on mortality is enormous. The probability of dying for young children and adults has risen twotofour fold, and the expectation of life at birth has fallen by more than fourteen years. We describe these changes in a compact way using the interpretable parameters of the HeligmanPollard mortality model. A Bayesian method is used to fit this model to periodsexagespecific mortality to yield probability distributions for the eight parameters that govern the model, for periodsexagespecific mortality and for all other columns of the corresponding life tables. Trends in the central estimates of the parameters are compared to the trend in HIV prevalence to suggest the impact of HIV on mortality. Probability distributions of the resulting
DOI: 10.4054/DemRes.2013.29.39
, 2013
"... The age pattern of increases in mortality affected by HIV: Bayesian fit of the HeligmanPollard Model to data from the Agincourt HDSS field site in rural northeast South Africa ..."
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The age pattern of increases in mortality affected by HIV: Bayesian fit of the HeligmanPollard Model to data from the Agincourt HDSS field site in rural northeast South Africa