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By
O'Neill, Philip D.
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5 Citations
The ReedFrost epidemic model is a simple stochastic process with parameter q that describes the spread of an infectious disease among a closed population. Given data on the final outcome of an epidemic, it is possible to perform Bayesian inference for q using a simple Gibbs sampler algorithm. In this paper it is illustrated that by choosing latent variables appropriately, certain monotonicity properties hold which facilitate the use of a perfect simulation algorithm. The methods are applied to real data.
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By
Kashiwagi, Nobuhisa
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4 Citations
A Bayesian solution is given to the problem of making inferences about an unknown number of structural changes in a sequence of observations. Inferences are based on the posterior distribution of the number of change points and on the posterior probabilities of possible change points. Detailed analyses are given for binomial data and some regression problems, and numerical illustrations are provided. In addition, an approximation procedure to compute the posterior probabilities is presented.
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By
Li, Lingge; Holbrook, Andrew; Shahbaba, Babak; Baldi, Pierre
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Hamiltonian Monte Carlo is a widely used algorithm for sampling from posterior distributions of complex Bayesian models. It can efficiently explore highdimensional parameter spaces guided by simulated Hamiltonian flows. However, the algorithm requires repeated gradient calculations, and these computations become increasingly burdensome as data sets scale. We present a method to substantially reduce the computation burden by using a neural network to approximate the gradient. First, we prove that the proposed method still maintains convergence to the true distribution though the approximated gradient no longer comes from a Hamiltonian system. Second, we conduct experiments on synthetic examples and real data to validate the proposed method.
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By
Shin, Seung Jun; Ghosh, Sujit K.
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With a quantal response, the doseresponse relation is summarized by the response probability function (RPF) that provides probabilities of the response being reacted as a function of dose levels. In the doseresponse analysis (DRA), it is often of primary interest to find a dose at which targeted response probability is attained, which we call target dose (TD). The estimation of the TD clearly depends on the underlying RPF structure. In this article, we provide a comparative analysis of some of the existing and newly proposed RPF estimation methods with particular emphasis on TD estimation. Empirical performances based on simulated data are presented to compare the existing and newly proposed methods. Nonparametric models based on a sequence of Bernstein polynomials are found to be robust against model misspecification. The methods are also illustrated using data obtained from a toxicological study.
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By
Meligkotsidou, Loukia
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8 Citations
In this paper we present Bayesian analysis of finite mixtures of multivariate Poisson distributions with an unknown number of components. The multivariate Poisson distribution can be regarded as the discrete counterpart of the multivariate normal distribution, which is suitable for modelling multivariate count data. Mixtures of multivariate Poisson distributions allow for overdispersion and for negative correlations between variables. To perform Bayesian analysis of these models we adopt a reversible jump Markov chain Monte Carlo (MCMC) algorithm with birth and death moves for updating the number of components. We present results obtained from applying our modelling approach to simulated and real data. Furthermore, we apply our approach to a problem in multivariate disease mapping, namely joint modelling of diseases with correlated counts.
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By
Miladinovic, Branko; Tsokos, Chris P.
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Extreme value distributions are increasingly being applied in biomedical literature to model unusual behavior or rare events. Two popular methods that are used to estimate the location and scale parameters of the type I extreme value (or Gumbel) distribution, namely, the empirical distribution function and the method of moments, are not optimal, especially for small samples. Additionally, even with the more robust maximum likelihood method, it is difficult to make inferences regarding outcomes based on estimates of location and scale parameters alone. Quantile modeling has been advocated in statistical literature as an intuitive and comprehensive approach to inferential statistics. We derive Bayesian estimates of the Gumbel quantile function by utilizing the Jeffreys noninformative prior and Lindley approximation procedure. The advantage of this approach is that it utilizes information on the prior distribution of parameters, while making minimal impact on the estimated posterior distribution. The Bayesian and maximum likelihood estimates are compared using numerical simulation. Numerical results indicate that Bayesian quantile estimates are closer to the true quantiles than their maximum likelihood counterparts. We illustrate the method by applying the estimates to published extreme data from the analysis of streak artifacts on computed tomography (CT) images.
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By
Yan, Jun; Cowles, Mary Kathryn; Wang, Shaowen; Armstrong, Marc P.
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30 Citations
When MCMC methods for Bayesian spatiotemporal modeling are applied to large geostatistical problems, challenges arise as a consequence of memory requirements, computing costs, and convergence monitoring. This article describes the parallelization of a reparametrized and marginalized posterior sampling (RAMPS) algorithm, which is carefully designed to generate posterior samples efficiently. The algorithm is implemented using the Parallel Linear Algebra Package (PLAPACK). The scalability of the algorithm is investigated via simulation experiments that are implemented using a cluster with 25 processors. The usefulness of the method is illustrated with an application to sulfur dioxide concentration data from the Air Quality System database of the U.S. Environmental Protection Agency.
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By
Ghosh, Sujit K.; Ebrahimi, Nader
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Changepoint hazard rate models arise, for example, in applying “burnin” techniques to screen defective items and in studying times until undesirable side effects occur in clinical trials. The classical approach develops estimates of model parameters, with particular interest in the threshold or changepoint parameter, but exclusively in terms of asymptotic properties. Such asymptotics can be poor for small to moderate sample sizes often encountered in practice. We propose a Bayesian approach, avoiding asymptotics, to provide more reliable inference conditional only upon the data actually observed. The Bayesian models can be fitted using simulation methods. We develop a very general formulation of the model but also look at special cases which offer particularly simple fitting. We illustrate with an application involving failure times of electrical insulation.
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By
Andreev, A.; Arjas, E.
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3 Citations
The study is based on a sample of 965 children living in Oulu region (Finland), who were monitored for acute middle ear infections from birth to the age of two years. We introduce a nonparametrically defined intensity model for ear infections, which involves both fixed and time dependent covariates, such as calendar time, current age, length of breastfeeding time until present, or current type of day care. Unmeasured heterogeneity, which manifests itself in frequent infections in some children and rare in others and which cannot be explained in terms of the known covariates, is modelled by using individual frailty parameters. A Bayesian approach is proposed to solve the inferential problem. The numerical work is carried out by Monte Carlo integration (MetropolisHastings algorithm).
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By
Tsionas, Efthymios G.
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The purpose of the paper, is to explain how recent advances in Markov Chain Monte Carlo integration can facilitate the routine Bayesian analysis of the linear model when the prior distribution is completely user dependent. The method is based on a MetropolisHastings algorithm with a Studentt source distribution that can generate posterior moments as well as marginal posterior densities for model parameters. The method is illustrated with numerical examples where the combination of prior and likelihood information leads to multimodal posteriors due to priorlikelihood conflicts, and to cases where prior information can be summarized by symmetric stable Paretian distributions.
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