Modelos alternativos para detecção de locos de características quantitativas (QTL) de carcaça e crescimento nos cromossomos 4, 5 e 7 de suínos

O conhecimento do genoma pode auxiliar na identificação de regiões cromossômicas e, eventualmente, de genes que controlam características quantitativas (QTLs) de importância econômica. em um experimento com 1.129 suínos resultantes do cruzamento entre machos da raça Meishan e fêmeas Large White e Landrace, foram analisadas as características gordura intramuscular (GIM), em %, e ganho dos 25 aos 90 kg de peso vivo (GP), em g/dia, em 298 animais F1 e 831 F2, e espessura de toucinho (ET), em mm, em 324 F1 e 805 F2. Os animais das gerações F1 e F2 foram tipificados com 29 marcadores microsatélites. Estudou-se a ligação entre os cromossomos 4, 6 e 7 com GIM, ET e GP. Análises de QTL utilizando-se metodologia Bayesiana foram aplicadas mediante três modelos genéticos: modelo poligênico infinitesimal (MPI); modelo poligênico finito (MPF), considerando-se três locos; e MPF combinado com MPI. O número de QTLs, suas respectivas posições nos três cromossomos e o efeito fenotípico foram estimados simultaneamente. Os sumários dos parâmetros estimados foram baseados nas distribuições marginais a posteriori, obtidas por meio do uso da Cadeia de Markov, algoritmos de Monte Carlo (MCMC). Foi possível evidenciar dois QTLs relacionados a GIM nos cromossomos 4 e 6 e dois a ET nos cromossomos 4 e 7. Somente quando se ajustou o MPI, foram observados QTLs no cromossomo 4 para ET e GIM. Não foi possível detectar QTLs para a característica GP com a aplicação dessa metodologia, o que pode ter resultado do uso de marcadores não informativos ou da ausência de QTLs segregando nos cromossomos 4, 6 e 7 desta população. Foi evidenciada a vantagem de se analisar dados experimentais ajustando diferentes modelos genéticos; essas análises ilustram a utilidade e ampla aplicabilidade do método Bayesiano.

Joint (X)over-bar and R charts with variable sample sizes and sampling intervals

Recent studies have shown that the (X) over bar chart with variable sampling intervals (VSI) and/or with variable sample sizes (VSS) detects process shifts faster than the traditional (X) over bar chart. This article extends these studies for processes that are monitored by both the (X) over bar and R charts. A Markov chain model is used to determine the properties of the joint (X) over bar and R charts with variable sample sizes and sampling intervals (VSSI). The VSSI scheme improves the joint (X) over bar and R control chart performance in terms of the speed with which shifts in the process mean and/or variance are detected.

Adaptive control charts: A Markovian approach for processes subject to independent disturbances

Recent studies have shown that adaptive X control charts are quicker than traditional X charts in detecting small to moderate shifts in a process. In this article, we propose a joint statistical design of adaptive X and R charts having all design parameters varying adaptively. The process is subjected to two independent assignable causes. One cause changes the process mean and the other changes the process variance. However, the occurrence of one kind of assignable cause does not preclude the occurrence of the other. It is assumed that the quality characteristic is normally distributed and the time that the process remains in control has exponential distribution. Performance measures of these adaptive control charts are obtained through a Markov chain approach. (c) 2005 Elsevier B.V. All rights reserved.

Robust Bayesian analysis of heavy-tailed stochastic volatility models using scale mixtures of normal distributions

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Bayesian outlier analysis in binary regression

We propose alternative approaches to analyze residuals in binary regression models based on random effect components. Our preferred model does not depend upon any tuning parameter, being completely automatic. Although the focus is mainly on accommodation of outliers, the proposed methodology is also able to detect them. Our approach consists of evaluating the posterior distribution of random effects included in the linear predictor. The evaluation of the posterior distributions of interest involves cumbersome integration, which is easily dealt with through stochastic simulation methods. We also discuss different specifications of prior distributions for the random effects. The potential of these strategies is compared in a real data set. The main finding is that the inclusion of extra variability accommodates the outliers, improving the adjustment of the model substantially, besides correctly indicating the possible outliers.

Bayesian estimation of generalized exponential distribution under noninformative priors

The generalized exponential distribution, proposed by Gupta and Kundu (1999), is a good alternative to standard lifetime distributions as exponential, Weibull or gamma. Several authors have considered the problem of Bayesian estimation of the parameters of generalized exponential distribution, assuming independent gamma priors and other informative priors. In this paper, we consider a Bayesian analysis of the generalized exponential distribution by assuming the conventional non-informative prior distributions, as Jeffreys and reference prior, to estimate the parameters. These priors are compared with independent gamma priors for both parameters. The comparison is carried out by examining the frequentist coverage probabilities of Bayesian credible intervals. We shown that maximal data information prior implies in an improper posterior distribution for the parameters of a generalized exponential distribution. It is also shown that the choice of a parameter of interest is very important for the reference prior. The different choices lead to different reference priors in this case. Numerical inference is illustrated for the parameters by considering data set of different sizes and using MCMC (Markov Chain Monte Carlo) methods.

The Poisson-exponential distribution: a Bayesian approach

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

A hierarchy of adaptive (X)over-bar control charts

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Probability distribution models for daily rainfall data for an interior station of Brazil

Two stochastic models have been fitted to daily rainfall data for an interior station of Brazil. Of these two models, the results show a better fit to describe the data, by truncated negative probability model in comparison with Markov chain probability model. Kolmogorov-Smirnov test is applied for significance for these models. © 1983 Springer-Verlag.

Joint X̄ and R Charts with Variable Sample Sizes and Sampling Intervals

Recent studies have shown that the X̄ chart with variable sampling intervals (VSI) and/or with variable sample sizes (VSS) detects process shifts faster than the traditional X̄ chart. This article extends these studies for processes that are monitored by both the X̄ and R charts. A Markov chain model is used to determine the properties of the joint X and R charts with variable sample sizes and sampling intervals (VSSI). The VSSI scheme improves the joint X̄ and R control chart performance in terms of the speed with which shifts in the process mean and/or variance are detected.

Robust linear mixed models with normal/independent distributions and Bayesian MCMC implementation

Linear mixed effects models have been widely used in analysis of data where responses are clustered around some random effects, so it is not reasonable to assume independence between observations in the same cluster. In most biological applications, it is assumed that the distributions of the random effects and of the residuals are Gaussian. This makes inferences vulnerable to the presence of outliers. Here, linear mixed effects models with normal/independent residual distributions for robust inferences are described. Specific distributions examined include univariate and multivariate versions of the Student-t, the slash and the contaminated normal. A Bayesian framework is adopted and Markov chain Monte Carlo is used to carry out the posterior analysis. The procedures are illustrated using birth weight data on rats in a texicological experiment. Results from the Gaussian and robust models are contrasted, and it is shown how the implementation can be used for outlier detection. The thick-tailed distributions provide an appealing robust alternative to the Gaussian process in linear mixed models, and they are easily implemented using data augmentation and MCMC techniques.

Stochastic Stability for Markovian Jump Linear Systems Subject to a Crucial Failure Event

This paper is concerned with the stability of discrete-time linear systems subject to random jumps in the parameters, described by an underlying finite-state Markov chain. In the model studied, a stopping time τ Δ is associated with the occurrence of a crucial failure after which the system is brought to a halt for maintenance. The usual stochastic stability concepts and associated results are not indicated, since they are tailored to pure infinite horizon problems. Using the concept named stochastic τ-stability, equivalent conditions to ensure the stochastic stability of the system until the occurrence of τ Δ is obtained. In addition, an intermediary and mixed case for which τ represents the minimum between the occurrence of a fix number N of failures and the occurrence of a crucial failure τ Δ is also considered. Necessary and sufficient conditions to ensure the stochastic τ-stability are provided in this setting that are auxiliary to the main result.

The LQ control problem for Markovian jumps linear systems with horizon defined by stopping times

This paper deals with a stochastic optimal control problem involving discrete-time jump Markov linear systems. The jumps or changes between the system operation modes evolve according to an underlying Markov chain. In the model studied, the problem horizon is defined by a stopping time τ which represents either, the occurrence of a fix number N of failures or repairs (TN), or the occurrence of a crucial failure event (τΔ), after which the system is brought to a halt for maintenance. In addition, an intermediary mixed case for which T represents the minimum between TN and τΔ is also considered. These stopping times coincide with some of the jump times of the Markov state and the information available allows the reconfiguration of the control action at each jump time, in the form of a linear feedback gain. The solution for the linear quadratic problem with complete Markov state observation is presented. The solution is given in terms of recursions of a set of algebraic Riccati equations (ARE) or a coupled set of algebraic Riccati equation (CARE).

A synthetic control chart for monitoring the process mean and variance

Purpose - The aim of this paper is to present a synthetic chart based on the non-central chi-square statistic that is operationally simpler and more effective than the joint X̄ and R chart in detecting assignable cause(s). This chart will assist in identifying which (mean or variance) changed due to the occurrence of the assignable causes. Design/methodology/approach - The approach used is based on the non-central chi-square statistic and the steady-state average run length (ARL) of the developed chart is evaluated using a Markov chain model. Findings - The proposed chart always detects process disturbances faster than the joint X̄ and R charts. The developed chart can monitor the process instead of looking at two charts separately. Originality/value - The most important advantage of using the proposed chart is that practitioners can monitor the process by looking at only one chart instead of looking at two charts separately. © Emerald Group Publishing Limted.

Segmentação de dados de perfilamento a laser em áreas urbanas utilizando uma abordagem Bayesiana

In this paper is presented a region-based methodology for Digital Elevation Model segmentation obtained from laser scanning data. The methodology is based on two sequential techniques, i.e., a recursive splitting technique using the quad tree structure followed by a region merging technique using the Markov Random Field model. The recursive splitting technique starts splitting the Digital Elevation Model into homogeneous regions. However, due to slight height differences in the Digital Elevation Model, region fragmentation can be relatively high. In order to minimize the fragmentation, a region merging technique based on the Markov Random Field model is applied to the previously segmented data. The resulting regions are firstly structured by using the so-called Region Adjacency Graph. Each node of the Region Adjacency Graph represents a region of the Digital Elevation Model segmented and two nodes have connectivity between them if corresponding regions share a common boundary. Next it is assumed that the random variable related to each node, follows the Markov Random Field model. This hypothesis allows the derivation of the posteriori probability distribution function whose solution is obtained by the Maximum a Posteriori estimation. Regions presenting high probability of similarity are merged. Experiments carried out with laser scanning data showed that the methodology allows to separate the objects in the Digital Elevation Model with a low amount of fragmentation.