- Department of Statistics
Athens University of Economics and Business
76 Patision Str, 10434, Athens, GREECE
http://stat-athens.aueb.gr/~jbn/ - +302108203968
Ioannis Ntzoufras
Athens University of Economics and Business, Statistics, Faculty Member
- Bayesian, Computational Statistics, Sports Statistics, MCMC, Computational Modelling, Biostatistics, and 12 moreApplied Statistics, Statistics, Mathematics, Econometrics, Applied Mathematics, Epidemiology, Medical Sciences, Data Mining, Latent variable modeling, Bayesian Analysis, Modeling and Simulation, and Psychometricsedit
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In this paper we present an R package called bivpois for maximum likelihood estimation of the parameters of bivariate and diagonal inflated bivariate Poisson regression models. An Expectation-Maximization (EM) algorithm is implemented.... more
In this paper we present an R package called bivpois for maximum likelihood estimation of the parameters of bivariate and diagonal inflated bivariate Poisson regression models. An Expectation-Maximization (EM) algorithm is implemented. Inflated models allow for modelling both over-dispersion (or under-dispersion) and negative correlation and thus they are appropriate for a wide range of applications. Extensions of the algorithms for several other models are also discussed. Detailed guidance and implementation on simulated and real data sets using bivpois package is provided.
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A stochastic search method, the so-called Adaptive Subspace (AdaSub) method, is proposed for variable selection in high-dimensional linear regression models. The method aims at finding the best model with respect to a certain model... more
A stochastic search method, the so-called Adaptive Subspace (AdaSub) method, is proposed for variable selection in high-dimensional linear regression models. The method aims at finding the best model with respect to a certain model selection criterion and is based on the idea of adaptively solving low-dimensional sub-problems in order to provide a solution to the original high-dimensional problem. Any of the usual $\ell_0$-type model selection criteria can be used, such as Akaike's Information Criterion (AIC), the Bayesian Information Criterion (BIC) or the Extended BIC (EBIC), with the last being particularly suitable for high-dimensional cases. The limiting properties of the new algorithm are analysed and it is shown that, under certain conditions, AdaSub converges to the best model according to the considered criterion. In a simulation study, the performance of AdaSub is investigated in comparison to alternative methods. The effectiveness of the proposed method is illustrated...
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This paper deals with the Bayesian analysis of graphical models of marginal independence for three way contingency tables. We use a marginal log-linear parametrization, under which the model is defined through suitable zero-constraints on... more
This paper deals with the Bayesian analysis of graphical models of marginal independence for three way contingency tables. We use a marginal log-linear parametrization, under which the model is defined through suitable zero-constraints on the interaction parameters calculated within marginal distributions. We undertake a comprehensive Bayesian analysis of these models, involving suitable choices of prior distributions, estimation, model determination, as well as the allied computational issues. The methodology is illustrated with reference to two real data sets.
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A simple and efficient adaptive Markov Chain Monte Carlo (MCMC) method, called the Metropolized Adaptive Subspace (MAdaSub) algorithm, is proposed for sampling from high-dimensional posterior model distributions in Bayesian variable... more
A simple and efficient adaptive Markov Chain Monte Carlo (MCMC) method, called the Metropolized Adaptive Subspace (MAdaSub) algorithm, is proposed for sampling from high-dimensional posterior model distributions in Bayesian variable selection. The MAdaSub algorithm is based on an independent Metropolis-Hastings sampler, where the individual proposal probabilities of the explanatory variables are updated after each iteration using a form of Bayesian adaptive learning, in a way that they finally converge to the respective covariates’ posterior inclusion probabilities. We prove the ergodicity of the algorithm and present a parallel version of MAdaSub with an adaptation scheme for the proposal probabilities based on the combination of information from multiple chains. The effectiveness of the algorithm is demonstrated via various simulated and real data examples, including a high-dimensional problem with more than 20,000 covariates.
A well known identifiability issue in factor analytic models is the invariance with respect to orthogonal transformations. This problem burdens the inference under a Bayesian setup, where Markov chain Monte Carlo (MCMC) methods are used... more
A well known identifiability issue in factor analytic models is the invariance with respect to orthogonal transformations. This problem burdens the inference under a Bayesian setup, where Markov chain Monte Carlo (MCMC) methods are used to generate samples from the posterior distribution. We introduce a post-processing scheme in order to deal with rotation, sign and permutation invariance of the MCMC sample. The exact version of the contributed algorithm requires to solve $2^q$ assignment problems per (retained) MCMC iteration, where $q$ denotes the number of factors of the fitted model. For large numbers of factors two approximate schemes based on simulated annealing are also discussed. We demonstrate that the proposed method leads to interpretable posterior distributions using synthetic and publicly available data from typical factor analytic models as well as mixtures of factor analyzers. An R package is available online at CRAN web-page.
Epidemic data often possess certain characteristics, such as the presence of many zeros, the spatial nature of the disease spread mechanism, environmental noise, serial correlation and dependence on time-varying factors. This paper... more
Epidemic data often possess certain characteristics, such as the presence of many zeros, the spatial nature of the disease spread mechanism, environmental noise, serial correlation and dependence on time-varying factors. This paper addresses these issues via suitable Bayesian modelling. In doing so, we utilize a general class of stochastic regression models appropriate for spatio-temporal count data with an excess number of zeros. The developed regression framework does incorporate serial correlation and time-varying covariates through an Ornstein-Uhlenbeck process formulation. In addition, we explore the effect of different priors, including default options and variations of mixtures of g-priors. The effect of different distance kernels for the epidemic model component is investigated. We proceed by developing branching process-based methods for testing scenarios for disease control, thus linking traditional epidemiological models with stochastic epidemic processes, useful in polic...
Research Interests: Computer Science, Statistics, Biostatistics, Medicine, Greece, and 15 moreHumans, Sheep, Animals, Regression Analysis, Branching Processes, Disease Control, SHEEP DISEASES, Branching Process, Bayes Theorem, Bayesian Modeling, Epidemics, Bayesian variable selection, epidemic extinction, spatial kernel, and Capripoxvirus
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This paper focuses on the Bayesian model average (BMA) using the power–expected– posterior prior in objective Bayesian variable selection under normal linear models. We derive a BMA point estimate of a predicted value, and present... more
This paper focuses on the Bayesian model average (BMA) using the power–expected– posterior prior in objective Bayesian variable selection under normal linear models. We derive a BMA point estimate of a predicted value, and present computation and evaluation strategies of the prediction accuracy. We compare the performance of our method with that of similar approaches in a simulated and a real data example from economics.
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Power-expected-posterior (PEP) priors have been recently introduced as generalized versions of the expected-posterior-priors (EPPs) for variable selection in Gaussian linear models. They are minimally-informative priors that reduce the... more
Power-expected-posterior (PEP) priors have been recently introduced as generalized versions of the expected-posterior-priors (EPPs) for variable selection in Gaussian linear models. They are minimally-informative priors that reduce the effect of training samples under the EPP approach, by combining ideas from the power-prior and unit-information-prior methodologies. In this paper we prove the information consistency of the PEP methodology, when using the independence Jeffreys as a baseline prior, for the variable selection problem in normal linear models.
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ABSTRACT We develop a Markov chain Monte Carlo algorithm, based on ‘stochastic search variable selection’ (George and McCuUoch, 1993), for identifying promising log-linear models. The method may be used in the analysis of multi-way... more
ABSTRACT We develop a Markov chain Monte Carlo algorithm, based on ‘stochastic search variable selection’ (George and McCuUoch, 1993), for identifying promising log-linear models. The method may be used in the analysis of multi-way contingency tables where the set of plausible models is very large.
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This paper deals with the Bayesian analysis of graphical models of marginal independence for three way contingency tables. We use a marginal log-linear parametrization, under which the model is defined through suitable zero-constraints on... more
This paper deals with the Bayesian analysis of graphical models of marginal independence for three way contingency tables. We use a marginal log-linear parametrization, under which the model is defined through suitable zero-constraints on the interaction parameters calculated within marginal distributions. We undertake a comprehensive Bayesian analysis of these models, involving suitable choices of prior distributions, estimation, model determination, as well as the allied computational issues. The methodology is illustrated with reference to two real data sets.
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Ntzoufras, I., Dellaportas, P. and Forster, JJ (1997) A comparison of Markov chain Monte Carlo methods for log-linear model selection. In, Lipitakis, EA (ed.) Proceedings of the 3rd Hellenic-European Conference on Mathematics and... more
Ntzoufras, I., Dellaportas, P. and Forster, JJ (1997) A comparison of Markov chain Monte Carlo methods for log-linear model selection. In, Lipitakis, EA (ed.) Proceedings of the 3rd Hellenic-European Conference on Mathematics and Informatics. 3rd Hellenic-European Conference on Mathematics and Informatics Athens, Greece, LEA, 506-514. ... Full text not available from this repository. ... RDF+N-Triples, RDF+N3, RDF+XML, Browse.
Bayesian analysis of correlated binary data when individual information is not available is considered. In particular, a binary outcome is measured on the same subjects of two independent groups at two separate occasions (usually time... more
Bayesian analysis of correlated binary data when individual information is not available is considered. In particular, a binary outcome is measured on the same subjects of two independent groups at two separate occasions (usually time points). The groups are formulated through a binary exposure or a prognostic factor. Interest lies in estimating the association between exposure and outcome over time. Standard methods for this purpose apply on the individual item responses and are insufficient in case these are missing. ...
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A hands-on introduction to the principles of Bayesian modeling using WinBUGS Bayesian Modeling Using WinBUGS provides an easily accessible introduction to the use of WinBUGS programming techniques in a variety of Bayesian modeling... more
A hands-on introduction to the principles of Bayesian modeling using WinBUGS Bayesian Modeling Using WinBUGS provides an easily accessible introduction to the use of WinBUGS programming techniques in a variety of Bayesian modeling settings. The author provides an accessible treatment of the topic, offering readers a smooth introduction to the principles of Bayesian modeling with detailed guidance on the practical implementation of key principles. The book begins with a basic introduction to Bayesian inference and the ...
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The Zellner's g-prior and its recent hierarchical extensions are the most popular default prior choices in the Bayesian variable selection context. These prior set-ups can be expressed power-priors with fixed set of imaginary data. In... more
The Zellner's g-prior and its recent hierarchical extensions are the most popular default prior choices in the Bayesian variable selection context. These prior set-ups can be expressed power-priors with fixed set of imaginary data. In this paper, we borrow ideas from the power-expected-posterior (PEP) priors in order to introduce, under the g-prior approach, an extra hierarchical level that accounts for the imaginary data uncertainty. For normal regression variable selection problems, the resulting power-conditional-expected-posterior (PCEP) prior is a conjugate normal-inverse gamma prior which provides a consistent variable selection procedure and gives support to more parsimonious models than the ones supported using the g-prior and the hyper-g prior for finite samples. Detailed illustrations and comparisons of the variable selection procedures using the proposed method, the g-prior and the hyper-g prior are provided using both simulated and real data examples.
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The problem of transformation selection is thoroughly treated from a Bayesian perspective. Several families of transformations are considered with a view to achieving normality: the Box-Cox, the Modulus, the Yeo & Johnson and the Dual... more
The problem of transformation selection is thoroughly treated from a Bayesian perspective. Several families of transformations are considered with a view to achieving normality: the Box-Cox, the Modulus, the Yeo & Johnson and the Dual transformation. Markov chain Monte Carlo algorithms have been constructed in order to sample from the posterior distribution of the transformation parameter $\lambda_T$ associated with each competing family $T$. We investigate different approaches to constructing compatible prior distributions for $\lambda_T$ over alternative transformation families, using a unit-information power-prior approach and an alternative normal prior with approximate unit-information interpretation. Selection and discrimination between different transformation families is attained via posterior model probabilities. We demonstrate the efficiency of our approach using a variety of simulated datasets. Although there is no choice of transformation family that can be universally applied to all problems, empirical evidence suggests that some particular data structures are best treated by specific transformation families. For example, skewness is associated with the Box-Cox family while fat-tailed distributions are efficiently treated using the Modulus transformation.
Although competitive balance is an important concept for professional team sports, its quantification still remains an issue. The main objective of this study is to identify the best or optimal index for the study of competitive balance... more
Although competitive balance is an important concept for professional team sports, its quantification still remains an issue. The main objective of this study is to identify the best or optimal index for the study of competitive balance in European football using a number of economic variables and data from eight domestic leagues from 1959 to 2008. The findings that refer to the indices specially designed to capture the complex structure of European football support the longstanding Uncertainty of Outcome Hypothesis. The most comprehensive bi-dimensional Special Dynamic Concentration index has the greatest effect on attendance while ranking mobility across seasons is more important for fans than seasonal performance.
The power-conditional-expected-posterior (PCEP) prior developed for variable selection in normal regression models combines ideas from the power-prior and expected-posterior prior, relying on the concept of random imaginary data, and... more
The power-conditional-expected-posterior (PCEP) prior developed for variable selection in normal regression models combines ideas from the power-prior and expected-posterior prior, relying on the concept of random imaginary data, and provides a consistent variable selection method which leads to parsimonious inference. In this paper we discuss the computational limitations of applying the PCEP prior to generalized linear models (GLMs) and present two PCEP prior variations which are easily applicable to regression models belonging to the exponential family of distributions. We highlight the differences between the initial PCEP prior and the two GLM-based PCEP prior adaptations and compare their properties in the conjugate case of the normal linear regression model. Hyper prior extensions for the PCEP power parameter are further considered. We consider several simulation scenarios and one real data example for evaluating the performance of the proposed methods compared to other common...
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ABSTRACT The marginal likelihood can be notoriously difficult to compute, and particularly so in high-dimensional problems. Chib and Jeliazkov employed the local reversibility of the Metropolis–Hastings algorithm to construct an estimator... more
ABSTRACT The marginal likelihood can be notoriously difficult to compute, and particularly so in high-dimensional problems. Chib and Jeliazkov employed the local reversibility of the Metropolis–Hastings algorithm to construct an estimator in models where full conditional densities are not available analytically. The estimator is free of distributional assumptions and is directly linked to the simulation algorithm. However, it generally requires a sequence of reduced Markov chain Monte Carlo runs which makes the method computationally demanding especially in cases when the parameter space is large. In this article, we study the implementation of this estimator on latent variable models which embed independence of the responses to the observables given the latent variables (conditional or local independence). This property is employed in the construction of a multi-block Metropolis-within-Gibbs algorithm that allows to compute the estimator in a single run, regardless of the dimensionality of the parameter space. The counterpart one-block algorithm is also considered here, by pointing out the difference between the two approaches. The paper closes with the illustration of the estimator in simulated and real-life data sets.
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In this paper we implement a Markov chain Monte Carlo algorithm based on the stochastic search variable selection method of George and McCulloch (1993) for identifying promising subsets of manifest variables (items) for factor analysis... more
In this paper we implement a Markov chain Monte Carlo algorithm based on the stochastic search variable selection method of George and McCulloch (1993) for identifying promising subsets of manifest variables (items) for factor analysis models. The suggested algorithm is constructed by embedding in the usual factor analysis model a normal mixture prior for the model loadings with latent indicators used to identify not only which manifest variables should be included in the model but also how each manifest variable is associated with each factor. We further extend the suggested algorithm to allow for factor selection. We also develop a detailed procedure for the specification of the prior parameters values based on the practical significance of factor loadings using ideas from the original work of George and McCulloch (1993). A straightforward Gibbs sampler is used to simulate from the joint posterior distribution of all unknown parameters and the subset of variables with the highest posterior probability is selected. The proposed method is illustrated using real and simulated data sets.
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Aims In this work we develop novel hypothesis tests for association models for two way contingency tables. We focus on conjugate analysis for the uniform, row and column effect model which can be considered as Poisson log-linear or... more
Aims In this work we develop novel hypothesis tests for association models for two way contingency tables. We focus on conjugate analysis for the uniform, row and column effect model which can be considered as Poisson log-linear or Multinomial logit models. For the row-column model we will develop an MCMC based approach which will try to explore conditional conjugancy structures of the model. Finally, we will thoroughly examine the sensitivity of these approaches on prior parameters and will explore possibilities to implement objective Bayes techniques. Notation: In I × J Contingency tables • n ij : the observed cell counts • r i = j n ij : the row total • c j = i n ij : the column total • n = i j n ij : the grand total for all i = 1, 2, · · · , I and j = 1, 2, · · · , J. H 0 : there is no association between the two categories H 1 : there is association between the two categories M 0 : n|π i+ , π j+ ∼ Multinomial(n, π) π = π ij = π i+ × π T +j π i+ ∼ Dirichlet