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Jorgensen, Terrence D.; GarnierVillarreal, Mauricio; Pornprasermanit, Sunthud; Lee, Jaehoon
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We simulated Bayesian CFA models to investigate the power of PPP to detect model misspecification by manipulating sample size, strongly and weakly informative priors for nontarget parameters, degree of misspecification, and whether data were generated and analyzed as normal or ordinal. Rejection rates indicate that PPP lacks power to reject an inappropriate model unless priors are unrealistically restrictive (essentially equivalent to fixing nontarget parameters to zero) and both sample size and misspecification are quite large. We suggest researchers evaluate global fit without priors for nontarget parameters, then search for neglected parameters if PPP indicates poor fit.
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By
Chino, Naohito
A brief review is made of a body of extant asymmetric MDS models and methods, given a onemode, twoway asymmetric square relational data matrix whose elements are similarity or dissimilarity measures between objects, or a special twomode, threeway asymmetric relational data matrix which is composed of onemode, twoway asymmetric square relational data matrices, and several open problems are discussed.
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By
O'Neill, Philip D.
7 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
5 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
Christianson, Annette; Sivaganesan, Siva
Generalized linear mixed models are commonly used when modeling counts or dichotomous observations on subjects within clusters such as patients in hospitals. When the sample sizes at the cluster levels are large, Bayesian inference about parameters of generalized linear mixed models using Markov Chain Monte Carlo sampling can be computationally slow. Standard large sample approximations can provide reasonable approximation for inference about clusterlevel parameters which are near the “middle” but not necessarily for those parameters away from the middle. We provide an approach to simulating from the posterior distribution that gives better approximation when the sample sizes at the cluster levels are large and a multivariate normal prior or the default flat prior is used.
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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.
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
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.
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.
Show all (4)
31 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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