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In recent years, there has been a considerable interest to study count time series with a dependence structure and appearance of excess of zeros values. Such series are commonly encountered in diverse disciplines, such as economics, financial research, environmental science, public health, among others. In this paper, we propose a stationary p-order integer-valued autoregressive process with zero-inflated Poisson innovations, called the ZINAR(p) times series model. We study some of its theoretical properties and develop a Markov chain Monte Carlo (MCMC) algorithm for inferring parameters from Bayesian perspectives. Finally, we demonstrate the utility of proposed ZINAR(p) model through simulated and real data examples. [ABSTRACT FROM AUTHOR]

Feature selection arises in many areas of modern science. For example, in genomic research, we want to find the genes that can be used to separate tissues of different classes (e.g. cancer and normal). One approach is to fit regression/classification models with certain penalization. In the past decade, hyper-LASSO penalization (priors) have received increasing attention in the literature. However, fully Bayesian methods that use Markov chain Monte Carlo (MCMC) for regression/classification with hyper-LASSO priors are still in lack of development. In this paper, we introduce an MCMC method for learning multinomial logistic regression with hyper-LASSO priors. Our MCMC algorithm uses Hamiltonian Monte Carlo in a restricted Gibbs sampling framework. We have used simulation studies and real data to demonstrate the superior performance of hyper-LASSO priors compared to LASSO, and to investigate the issues of choosing heaviness and scale of hyper-LASSO priors. [ABSTRACT FROM AUTHOR]

The need to simulate from a univariate density arises in several settings, particularly in Bayesian analysis. An especially efficient algorithm which can be used to sample from a univariate density, fX, is the adaptive accept-reject algorithm. To implement the adaptive accept-reject algorithm, the user has to envelope T ∘ fX, where T is some transformation such that the density g(x) ∝ T-1 (α+β x) is easy to sample from. Successfully enveloping T ∘ fX, however, requires that the user identify the number and location of T ∘ fX's inflection points. This is not always a trivial task. In this paper, we propose an adaptive accept-reject algorithm which relieves the user of precisely identifying the location of T ∘ fX's inflection points. This new algorithm is shown to be efficient and can be used to sample from any density such that its support is bounded and its log is three-times differentiable. [ABSTRACT FROM AUTHOR]

This paper proposes a two-sided monitoring algorithm of changes in the exponential family. We adopt a Bayesian approach which uses a loss function and takes into account the run length of the process. It also extends the monitoring scheme proposed in [Harrison, P.J., Veerapen, P.P., 1994, A Bayesian decision approach to model monitoring and Cusums. Journal of Forecasting, 13, 29-36.] The algorithm is illustrated with several examples, which analyze the power of the monitor. [ABSTRACT FROM AUTHOR]

The full Bayesian significance test (FBST) was introduced by Pereira and Stern for measuring the evidence of a precise null hypothesis. The FBST requires both numerical optimization and multidimensional integration, whose computational cost may be heavy when testing a precise null hypothesis on a scalar parameter of interest in the presence of a large number of nuisance parameters. In this paper we propose a higher order approximation of the measure of evidence for the FBST, based on tail area expansions of the marginal posterior of the parameter of interest. When in particular focus is on matching priors, further results are highlighted. Numerical illustrations are discussed. [ABSTRACT FROM PUBLISHER]

Item response theory (IRT) comprises a set of statistical models which are useful in many fields, especially when there is an interest in studying latent variables (or latent traits). Usually such latent traits are assumed to be random variables and a convenient distribution is assigned to them. A very common choice for such a distribution has been the standard normal. Recently, Azevedo et al. [Bayesian inference for a skew-normal IRT model under the centred parameterization, Comput. Stat. Data Anal. 55 (2011), pp. 353–365] proposed a skew-normal distribution under the centred parameterization (SNCP) as had been studied in [R.B. Arellano-Valle and A. Azzalini, The centred parametrization for the multivariate skew-normal distribution, J. Multivariate Anal. 99(7) (2008), pp. 1362–1382], to model the latent trait distribution. This approach allows one to represent any asymmetric behaviour concerning the latent trait distribution. Also, they developed a Metropolis–Hastings within the Gibbs sampling (MHWGS) algorithm based on the density of the SNCP. They showed that the algorithm recovers all parameters properly. Their results indicated that, in the presence of asymmetry, the proposed model and the estimation algorithm perform better than the usual model and estimation methods. Our main goal in this paper is to propose another type of MHWGS algorithm based on a stochastic representation (hierarchical structure) of the SNCP studied in [N. Henze, A probabilistic representation of the skew-normal distribution, Scand. J. Statist. 13 (1986), pp. 271–275]. Our algorithm has only one Metropolis–Hastings step, in opposition to the algorithm developed by Azevedo et al., which has two such steps. This not only makes the implementation easier but also reduces the number of proposal densities to be used, which can be a problem in the implementation of MHWGS algorithms, as can be seen in [R.J. Patz and B.W. Junker, A straightforward approach to Markov Chain Monte Carlo methods for item response models, J. Educ. Behav. Stat. 24(2) (1999), pp. 146–178; R.J. Patz and B.W. Junker, The applications and extensions of MCMC in IRT: Multiple item types, missing data, and rated responses, J. Educ. Behav. Stat. 24(4) (1999), pp. 342–366; A. Gelman, G.O. Roberts, and W.R. Gilks, Efficient Metropolis jumping rules, Bayesian Stat. 5 (1996), pp. 599–607]. Moreover, we consider a modified beta prior (which generalizes the one considered in [3]) and a Jeffreys prior for the asymmetry parameter. Furthermore, we study the sensitivity of such priors as well as the use of different kernel densities for this parameter. Finally, we assess the impact of the number of examinees, number of items and the asymmetry level on the parameter recovery. Results of the simulation study indicated that our approach performed equally as well as that in [3], in terms of parameter recovery, mainly using the Jeffreys prior. Also, they indicated that the asymmetry level has the highest impact on parameter recovery, even though it is relatively small. A real data analysis is considered jointly with the development of model fitting assessment tools. The results are compared with the ones obtained by Azevedo et al. The results indicate that using the hierarchical approach allows us to implement MCMC algorithms more easily, it facilitates diagnosis of the convergence and also it can be very useful to fit more complex skew IRT models. [ABSTRACT FROM PUBLISHER]

An important problem in statistics is the study of longitudinal data taking into account the effect of other explanatory variables such as treatments and time. In this paper, a new Bayesian approach for analysing longitudinal data is proposed. This innovative approach takes into account the possibility of having nonlinear regression structures on the mean and linear regression structures on the variance-covariance matrix of normal observations, and it is based on the modelling strategy suggested by Pourahmadi [M. Pourahmadi, Joint mean-covariance models with applications to longitudinal data: Unconstrained parameterizations, Biometrika, 87 (1999), pp. 667-690.]. We initially extend the classical methodology to accommodate the fitting of nonlinear mean models then we propose our Bayesian approach based on a generalization of the Metropolis-Hastings algorithm of Cepeda [E.C. Cepeda, Variability modeling in generalized linear models, Unpublished Ph.D. Thesis, Mathematics Institute, Universidade Federal do Rio de Janeiro, 2001]. Finally, we illustrate the proposed methodology by analysing one example, the cattle data set, that is used to study cattle growth. [ABSTRACT FROM AUTHOR]

Assume that K independent copies are made from a common prototype DNA sequence whose length is a random variable. In this paper, the problem of aligning those copies and therefore the problem of estimating the prototype sequence that produced the copies is addressed. A hidden Markov chain is used to model the copying procedure, and a reversible jump Markov chain Monte Carlo algorithm is used to sample the parameters of the model from their posterior distribution. Using the sample obtained, the Bayesian model and the prototype sequence may be selected using the maximum a posteriori estimate. A prior distribution for the prototype DNA sequence that incorporates a correlation among neighbouring bases is also considered. In addition, an analysis of the performance of the algorithm is presented when different scenarios are taken into account. [ABSTRACT FROM AUTHOR]

Estimates from an EM algorithm are somewhat sensitive to the initial values for the estimates, and this sensitivity is likely to increase when the model becomes larger and more complicated. In this paper, we examined how the estimates fluctuate during an EM procedure for a recursive model of categorical variables. It is found that the fluctuation takes place mostly during the initial stage of the procedure and that it can be reduced by applying a Bayes method of estimation. Both real and simulated data are used for illustration. [ABSTRACT FROM AUTHOR]

Joint models are statistical tools for estimating the association between time-to-event and longitudinal outcomes. One challenge to the application of joint models is its computational complexity. Common estimation methods for joint models include a two-stage method, Bayesian and maximum-likelihood methods. In this work, we consider joint models of a time-to-event outcome and multiple longitudinal processes and develop a maximum-likelihood estimation method using the expectation–maximization algorithm. We assess the performance of the proposed method via simulations and apply the methodology to a data set to determine the association between longitudinal systolic and diastolic blood pressure measures and time to coronary artery disease. [ABSTRACT FROM AUTHOR]

Motivated by molecular biology, there has been an upsurge of research activities in directional statistics in general and its Bayesian aspect in particular. The central distribution for the circular case is von Mises distribution which has two parameters (mean and concentration) akin to the univariate normal distribution. However, there has been a challenge to sample efficiently from the posterior distribution of the concentration parameter. We describe a novel, highly efficient algorithm to sample from the posterior distribution and fill this long-standing gap. [ABSTRACT FROM AUTHOR]

We propose a new iterative algorithm, called model walking algorithm, to the Bayesian model averaging method on the longitudinal regression models with AR(1) random errors within subjects. The Markov chain Monte Carlo method together with the model walking algorithm are employed. The proposed method is successfully applied to predict the progression rates on a myopia intervention trial in children. [ABSTRACT FROM PUBLISHER]

It is well known that the approximate Bayesian computation algorithm based on Markov chain Monte Carlo methods suffers from the sensitivity to the choice of starting values, inefficiency and a low acceptance rate. To overcome these problems, this study proposes a generalization of the multiple-point Metropolis algorithm, which proceeds by generating multiple-dependent proposals and then by selecting a candidate among the set of proposals on the basis of weights that can be chosen arbitrarily. The performance of the proposed algorithm is illustrated by using both simulated and real data. [ABSTRACT FROM AUTHOR]

Solving label switching is crucial for interpreting the results of fitting Bayesian mixture models. The label switching originates from the invariance of posterior distribution to permutation of component labels. As a result, the component labels in Markov chain simulation may switch to another equivalent permutation, and the marginal posterior distribution associated with all labels may be similar and useless for inferring quantities relating to each individual component. In this article, we propose a new simple labelling method by minimizing the deviance of the class probabilities to a fixed reference labels. The reference labels can be chosen before running Markov chain Monte Carlo (MCMC) using optimization methods, such as expectation-maximization algorithms, and therefore the new labelling method can be implemented by an online algorithm, which can reduce the storage requirements and save much computation time. Using the Acid data set and Galaxy data set, we demonstrate the success of the proposed labelling method for removing the labelling switching in the raw MCMC samples. [ABSTRACT FROM PUBLISHER]

We present a Bayesian approach to modelling and estimating objects in three dimensions. A general stochastic model for object recognition based on points in the domain of observation is created via hierarchical mixtures, allowing for the inclusion of important prior information about the objects under consideration. Objects under consideration are created based on three-dimensional (3D) points in space, with each point having some probability of membership to different objects. This is the first object-oriented statistical approach that models 3D objects in a true 3D environment. A data-augmentation approach and a Birth–Death Markov Chain Monte Carlo algorithm are incorporated to provide classification probabilities of each data point to one or more of the identified objects and to obtain estimates of the parameters that describe each object. Strengths of the methodology include its ease in accommodating different data and process models, its flexibility in handling varying numbers of mixture components, and most importantly, its ability to allow for inference on individual characteristics of objects. These strengths are demonstrated on an application for a forest (tree objects) near Olympia, WA, based on remotely sensed Light Detection and Ranging point observations. [ABSTRACT FROM PUBLISHER]

From the exact distribution of the maximum likelihood estimator of the average lifetime based on progressive hybrid exponential censored sample, we derive an explicit expression for the Bayes risk of a sampling plan when a quadratic loss function is used. The simulated annealing algorithm is then used to determine the optimal sampling plan. Some optimal Bayes solutions under progressive hybrid and ordinary hybrid censoring schemes are presented to illustrate the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

Considers a Bayesian analysis of the three-stage hierarchical multinomial model. Implementation of the Metropolis-Hasting algorithm; Comparisons with Gibbs and Laplace approximation; Applications of multi-stage hierarchical models.