Search

Skew-normal distribution is a class of distributions that includes the normal distributions as a special case. In this paper, we explore the use of Markov Chain Monte Carlo (MCMC) methods to develop a Bayesian analysis in a multivariate, null intercept, measurement error model [R. Aoki, H. Bolfarine, J.A. Achcar, and D. Leao Pinto Jr, Bayesian analysis of a multivariate null intercept error-in-variables regression model, J. Biopharm. Stat. 13(4) (2003b), pp. 763-771] where the unobserved value of the covariate (latent variable) follows a skew-normal distribution. The results and methods are applied to a real dental clinical trial presented in [A. Hadgu and G. Koch, Application of generalized estimating equations to a dental randomized clinical trial, J. Biopharm. Stat. 9 (1999), pp. 161-178]. [ABSTRACT FROM AUTHOR]

In this paper the issue of making inferences with misclassified data from a noisy multinomial process is addressed. A Bayesian model for making inferences about the proportions and the noise parameters is developed. The problem is reformulated in a more tractable form by introducing auxiliary or latent random vectors. This allows for an easy-to-implement Gibbs sampling-based algorithm to generate samples from the distributions of interest. An illustrative example related to elections is also presented. [ABSTRACT FROM AUTHOR]

Quasi-optimal procedures of testing many hypotheses are described in this paper. They significantly simplify the Bayesian algorithms of hypothesis testing and computation of the risk function. The relations allowing for obtaining the estimations for the values of average risks in optimum tasks are given. The obtained general solutions are reduced to concrete formulae for a multivariate normal distribution of probabilities. The methods of approximate computation of the risk functions in Bayesian tasks of testing many hypotheses are offered. The properties and interrelations of the developed methods and algorithms are investigated. On the basis of a simulation, the validity of the obtained results and conclusions drawn is presented. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a Bayesian Analysis for the Block and Basu bivariate exponential distribution using Markov Chain Monte Carlo (MCMC) methods and considering lifetimes in presence of covariates and censored data. Posterior summaries of interest are obtained using the popular WinBUGS software. Numerical illustrations are introduced considering a medical data set related to the recurrence times of infection for kidney patients and a medical data set related to bone marrow transplantation for leukemia. [ABSTRACT FROM AUTHOR]

Analyzing incomplete data for inferring the structure of gene regulatory networks (GRNs) is a challenging task in bioinformatic. Bayesian network can be successfully used in this field.k-nearest neighbor, singular value decomposition (SVD)-based and multiple imputation by chained equations are three fundamental imputation methods to deal with missing values. Path consistency (PC) algorithm based on conditional mutual information (PCA–CMI) is a famous algorithm for inferring GRNs. This algorithm needs the data set to be complete. However, the problem is that PCA–CMI is not a stable algorithm and when applied on permuted gene orders, different networks are obtained. We propose an order independent algorithm, PCA–CMI–OI, for inferring GRNs. After imputation of missing data, the performances of PCA–CMI and PCA–CMI–OI are compared. Results show that networks constructed from data imputed by the SVD-based method and PCA–CMI–OI algorithm outperform other imputation methods and PCA–CMI. An undirected or partially directed network is resulted by PC-based algorithms. Mutual information test (MIT) score, which can deal with discrete data, is one of the famous methods for directing the edges of resulted networks. We also propose a new score, ConMIT, which is appropriate for analyzing continuous data. Results shows that the precision of directing the edges of skeleton is improved by applying the ConMIT score. [ABSTRACT FROM PUBLISHER]

In this article, static light scattering (SLS) measurements are processed to estimate the particle size distribution of particle systems incorporating prior information obtained from an alternative experimental technique: scanning electron microscopy (SEM). For this purpose we propose two Bayesian schemes (one parametric and another non-parametric) to solve the stated light scattering problem and take advantage of the obtained results to summarize some features of the Bayesian approach within the context of inverse problems. The features presented in this article include the improvement of the results when some useful prior information from an alternative experiment is considered instead of a non-informative prior as it occurs in a deterministic maximum likelihood estimation. This improvement will be shown in terms of accuracy and precision in the corresponding results and also in terms of minimizing the effect of multiple minima by including significant information in the optimization. Both Bayesian schemes are implemented using Markov Chain Monte Carlo methods. They have been developed on the basis of the Metropolis–Hastings (MH) algorithm using Matlab®and are tested with the analysis of simulated and experimental examples of concentrated and semi-concentrated particles. In the simulated examples, SLS measurements were generated using a rigorous model, while the inversion stage was solved using an approximate model in both schemes and also using the rigorous model in the parametric scheme. Priors from SEM micrographs were also simulated and experimented, where the simulated ones were obtained using a Monte Carlo routine. In addition to the presentation of these features of the Bayesian approach, some other topics will be discussed, such as regularization and some implementation issues of the proposed schemes, among which we remark the selection of the parameters used in the MH algorithm. [ABSTRACT FROM AUTHOR]

We study the genotype calling algorithms for the high-throughput single-nucleotide polymorphism (SNP) arrays. Building upon the novel SNP-robust multi-chip average preprocessing approach and the state-of-the-art corrected robust linear model with Mahalanobis distance (CRLMM) approach for genotype calling, we propose a simple modification to better model and combine the information across multiple SNPs with empirical Bayes modeling, which could often significantly improve the genotype calling of CRLMM. Through applications to the HapMap Trio data set and a non-HapMap test set of high quality SNP chips, we illustrate the competitive performance of the proposed method. [ABSTRACT FROM AUTHOR]

Sex-related homicides tend to arouse wide media coverage and thus raise the urgency to find the responsible offender. However, due to the low frequency of such crimes, domain knowledge lacks completeness. We have therefore accumulated a large data-set and apply several structural learning algorithms to the data in order to combine their results into a single general graphic model. The graphical model broadly presents a distinction between an offender and a situation-driven crime. A situation-driven crime may be characterised by, amongst others, an offender lacking preparation and typically attacking a known victim in familiar surroundings. On the other hand, offender-driven crimes may be identified by the high level of forensic awareness demonstrated by the offender and the sophisticated measures applied to control the victim. The prediction performance of the graphical model is evaluated via a model averaging approach on the outcome variable offender's age. The combined graph undercuts the error rate of the single algorithms and an appropriate threshold results in an error rate of less than 10%, which describes a promising level for an actual implementation by the police. [ABSTRACT FROM AUTHOR]

We analyze the multivariate spatial distribution of plant species diversity, distributed across three ecologically distinct land uses, the urban residential, urban non-residential, and desert. We model these data using a spatial generalized linear mixed model. Here plant species counts are assumed to be correlated within and among the spatial locations. We implement this model across the Phoenix metropolis and surrounding desert. Using a Bayesian approach, we utilized the Langevin-Hastings hybrid algorithm. Under a generalization of a spatial log-Gaussian Cox model, the log-intensities of the species count processes follow Gaussian distributions. The purely spatial component corresponding to these log-intensities are jointly modeled using a cross-convolution approach, in order to depict a valid cross-correlation structure. We observe that this approach yields non-stationarity of the model ensuing from different land use types. We obtain predictions of various measures of plant diversity including plant richness and the Shannon-Weiner diversity at observed locations. We also obtain a prediction framework for plant preferences in urban and desert plots. [ABSTRACT FROM AUTHOR]

Joint generalized linear models and double generalized linear models (DGLMs) were designed to model outcomes for which the variability can be explained using factors and/or covariates. When such factors operate, the usual normal regression models, which inherently exhibit constant variance, will under-represent variation in the data and hence may lead to erroneous inferences. For count and proportion data, such noise factors can generate a so-called overdispersion effect, and the use of binomial and Poisson models underestimates the variability and, consequently, incorrectly indicate significant effects. In this manuscript, we propose a DGLM from a Bayesian perspective, focusing on the case of proportion data, where the overdispersion can be modeled using a random effect that depends on some noise factors. The posterior joint density function was sampled using Monte Carlo Markov Chain algorithms, allowing inferences over the model parameters. An application to a data set on apple tissue culture is presented, for which it is shown that the Bayesian approach is quite feasible, even when limited prior information is available, thereby generating valuable insight for the researcher about its experimental results. [ABSTRACT FROM AUTHOR]

It is known that patients may cease participating in a longitudinal study and become lost to follow-up. The objective of this article is to present a Bayesian model to estimate the malaria transition probabilities considering individuals lost to follow-up. We consider a homogeneous population, and it is assumed that the considered period of time is small enough to avoid two or more transitions from one state of health to another. The proposed model is based on a Gibbs sampling algorithm that uses information of lost to follow-up at the end of the longitudinal study. To simulate the unknown number of individuals with positive and negative states of malaria at the end of the study and lost to follow-up, two latent variables were introduced in the model. We used a real data set and a simulated data to illustrate the application of the methodology. The proposed model showed a good fit to these data sets, and the algorithm did not show problems of convergence or lack of identifiability. We conclude that the proposed model is a good alternative to estimate probabilities of transitions from one state of health to the other in studies with low adherence to follow-up. [ABSTRACT FROM AUTHOR]

The problem of change point in autoregressive process is studied in this article. We propose a Bayesian information criterion-iterated cumulative sums of squares algorithm to detect the variance changes in an autoregressive series with unknown order. Simulation results and two examples are presented, where it is shown to have good performances when the sample size is relatively small. [ABSTRACT FROM AUTHOR]

In this work we propose Bayesian measures to quantify the influence of observations on the structural parameters of the simple measurement error model (MEM). Different influence measures, like those based on q-divergence between posterior distributions and Bayes risk, are studied to evaluate the influence. A strategy based on the perturbation function and MCMC samples is used to compute these measures. The samples from the posterior distributions are obtained by using the Metropolis-Hastings algorithm and assuming specific proper prior distributions. The results are illustrated with an application to a real example modeled with MEM in the literature. [ABSTRACT FROM AUTHOR]

We investigate a Bayesian method for the segmentation of muscle fibre images. The images are reasonably well approximated by a Dirichlet tessellation, and so we use a deformable template model based on Voronoi polygons to represent the segmented image. We consider various prior distributions for the parameters and suggest an appropriate likelihood. Following the Bayesian paradigm, the mathematical form for the posterior distribution is obtained (up to an integrating constant). We introduce a Metropolis–Hastings algorithm and a reversible jump Markov chain Monte Carlo algorithm (RJMCMC) for simulation from the posterior when the number of polygons is fixed or unknown. The particular moves in the RJMCMC algorithm are birth, death and position/colour changes of the point process which determines the location of the polygons. Segmentation of the true image was carried out using the estimated posterior mode and posterior mean. A simulation study is presented which is helpful for tuning the hyperparameters and to assess the accuracy. The algorithms work well on a real image of a muscle fibre cross-section image, and an additional parameter, which models the boundaries of the muscle fibres, is included in the final model. [ABSTRACT FROM AUTHOR]

Bayesian analysis of panel data using a class of momentum threshold autoregressive (MTAR) models is considered. Posterior estimation of parameters of the MTAR models is done by using a simple Markov Chain Monte Carlo (MCMC) algorithm. Selection of appropriate differenced variables, test for asymmetry and unit roots are recast as model selections and a simple way of computing posterior probabilities of the candidate models is proposed. The proposed method is applied to the yearly unemployment rates of 51 US states and the results show strong evidence of stationarity and asymmetry. [ABSTRACT FROM AUTHOR]