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35
On Leverage in a Stochastic Volatility Model
 JOURNAL OF ECONOMETRICS
, 2005
"... This note is concerned with specification for modelling financial leverage effect in the context of stochastic volatility (SV) models. Two alternative specifications coexist in the literature. One is the Euler approximation to the well known continuous time SV model with leverage effect and the o ..."
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Cited by 28 (7 self)
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This note is concerned with specification for modelling financial leverage effect in the context of stochastic volatility (SV) models. Two alternative specifications coexist in the literature. One is the Euler approximation to the well known continuous time SV model with leverage effect and the other is the discrete time SV model of Jacquier, Polson and Rossi (2004, Journal of Econometrics, forthcoming). Using a Gaussian nonlinear state space form with uncorrelated measurement and transition errors, I show that it is easy to interpret the leverage e#ect in the conventional model whereas it is not clear how to obtain the leverage effect in the model of Jacquier et al. Empirical comparisons of these two models via Bayesian Markov chain Monte Carlo (MCMC) methods reveal that the specification of Jacquier et al is inferior. Simulation experiments are conducted to study the sampling properties of the Bayes MCMC for the conventional model.
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 24 (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
Multilevel models with multivariate mixed response types.” Statistical Modelling
, 2009
"... Abstract: We build upon the existing literature to formulate a class of models for multivariate mixtures of Gaussian, ordered or unordered categorical responses and continuous distributions that are not Gaussian, each of which can be defined at any level of a multilevel data hierarchy. We describe a ..."
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Cited by 2 (1 self)
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Abstract: We build upon the existing literature to formulate a class of models for multivariate mixtures of Gaussian, ordered or unordered categorical responses and continuous distributions that are not Gaussian, each of which can be defined at any level of a multilevel data hierarchy. We describe a Markov chain Monte Carlo algorithm for fitting such models. We show how this unifies a number of disparate problems, including partially observed data and missing data in generalized linear modelling. The twolevel model is considered in detail with worked examples of applications to a prediction problem and to multiple imputation for missing data. We conclude with a discussion outlining possible extensions and connections in the literature. Software for estimating the models is freely available. Key words: Box–Cox transformation; data augmentation; data coarsening; latent Gaussian model; maximum indicant model; MCMC; missing data; mixed response models; multilevel; multiple imputation; multivariate; normalising transformations; partially known values; prediction; priorinformed imputation; probit model
Bayesian Modeling of MPSS Data: Gene Expression Analysis of Bovine Salmonella Infection
"... Among the countingbased technologies available for gene expression profiling, massively parallel signature sequencing (MPSS) has some advantages over competitors such as serial analysis of gene expression (SAGE) or direct sequencing of cDNA and is ideal for building complex relational databases for ..."
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Among the countingbased technologies available for gene expression profiling, massively parallel signature sequencing (MPSS) has some advantages over competitors such as serial analysis of gene expression (SAGE) or direct sequencing of cDNA and is ideal for building complex relational databases for gene expression. Our goal is to compare the in vivo global gene expression profiles of tissues infected with different strains of Salmonella obtained using the MPSS technology. In this article, we develop an exact ANOVA type model for this count data using a zero inflated Poisson (ZIP) distribution, different from existing methods that assume continuous densities. We adopt two Bayesian hierarchical models—one parametric and the other semiparametric with a Dirichlet process prior that has the ability to “borrow strength ” across related signatures, where signature is a specific arrangement of the nucleotides, usually 1621 basepairs long. We utilize the discreteness of Dirichlet process prior to cluster signatures that exhibit similar differential expression profiles. Tests for differential expression are carriedout using nonparametric approaches, while controlling the false discovery rate. We identify several differentially expressed genes that have important biological significance and conclude with a summary of the biological discoveries.
MCMC Methods for Estimating Stochastic Volatility Models with Leverage Effects: Comments on
, 2002
"... In this note we represent the well known discrete time stochastic volatility (SV) model with a leverage effect and the SV model of Jacquier, Polson and Rossi (JPR) (2002) using Gaussian nonlinear state space forms with uncorrelated measurement and transition errors. With the new representations, we ..."
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In this note we represent the well known discrete time stochastic volatility (SV) model with a leverage effect and the SV model of Jacquier, Polson and Rossi (JPR) (2002) using Gaussian nonlinear state space forms with uncorrelated measurement and transition errors. With the new representations, we show that the JPR specification does not necessarily lead to a leverage effect and hence is not theoretically justified. Empirical comparisons of these two models via Bayesian MCMC methods reveal that JPR’s specification is not supported by actual data either. Simulation experiments are conducted to study the sampling properties of the Bayes estimator for the conventionally specified model.
A Bayesian Poisson Vector Autoregression Model ∗
, 2011
"... Multivariate count models are rare in political science, despite the presence of many count time series. This article develops a new Bayesian Poisson vector autoregression (BaPVAR) model that can characterize endogenous dynamic counts with no restrictions on the contemporaneous correlations. Impuls ..."
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Multivariate count models are rare in political science, despite the presence of many count time series. This article develops a new Bayesian Poisson vector autoregression (BaPVAR) model that can characterize endogenous dynamic counts with no restrictions on the contemporaneous correlations. Impulse responses, decomposition of the forecast errors, and dynamic multiplier methods for the effects of exogenous covariate shocks are illustrated for the model. Two full illustrations of the model, its interpretations, and results are presented. The first example is a dynamic model that reanalyzes the patterns and predictors of superpower rivalry events. The second example applies the model to analyze the dynamics of transnational terrorist targeting decisions between 1968 and 2008. The latter example’s results have direct implications for contemporary policy about terrorists ’ targeting that are both novel and innovative in the study of terrorism. This study was funded by the US Department of Homeland Security (DHS) through the Center for Risk