A Note on the Prior Distributions of Weibull Parameters for the Reliability Function

In Bayesian Inference it is often desirable to have a posterior density reflecting mainly the information from sample data. To achieve this purpose it is important to employ prior densities which add little information to the sample. We have in the literature many such prior densities, for example, Jeffreys (1967), Lindley (1956); (1961), Hartigan (1964), Bernardo (1979), Zellner (1984), Tibshirani (1989), etc. In the present article, we compare the posterior densities of the reliability function by using Jeffreys, the maximal data information (Zellner, 1984), Tibshirani's, and reference priors for the reliability function R(t) in a Weibull distribution.

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.

A Bayesian approach to estimate the accuracy of in-house ELISA assay to measure rabies antibodies from compulsory vaccinated dogs and cattle

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

A bayesian analysis for the parameters of the exponential-logarithmic distribution

The exponential-logarithmic is a new lifetime distribution with decreasing failure rate and interesting applications in the biological and engineering sciences. Thus, a Bayesian analysis of the parameters would be desirable. Bayesian estimation requires the selection of prior distributions for all parameters of the model. In this case, researchers usually seek to choose a prior that has little information on the parameters, allowing the data to be very informative relative to the prior information. Assuming some noninformative prior distributions, we present a Bayesian analysis using Markov Chain Monte Carlo (MCMC) methods. Jeffreys prior is derived for the parameters of exponential-logarithmic distribution and compared with other common priors such as beta, gamma, and uniform distributions. In this article, we show through a simulation study that the maximum likelihood estimate may not exist except under restrictive conditions. In addition, the posterior density is sometimes bimodal when an improper prior density is used. © 2013 Copyright Taylor and Francis Group, LLC.

Associações das concentrações séricas de ácido úrico com as variáveis dietéticas, antropométricas e bioquímicas de adultos clinicamente selecionados para programa de mudança de estilo de vida

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Lipoprotein Lipase and PPAR Alpha Gene Polymorphisms, Increased Very-Low-Density Lipoprotein Levels, and Decreased High-Density Lipoprotein Levels as Risk Markers for the Development of Visceral Leishmaniasis by Leishmania infantum

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Low Bone Mineral Density in Middle-Aged Breast Cancer Survivors: Prevalence and Associated Factors

Background: The aim of this study was to investigate the prevalence of low bone mineral density (BMD) and associated factors in middle-aged breast cancer survivors (BCS). Patients and Methods: A cross-sectional study was conducted with 70 BCS of 45-65 years of age undergoing complete oncology treatment. Logistic regression models were used to identify factors associated with low BMD (osteopenia and osteoporosis taken together as a single group). Results: The mean age of participants was 53.2 +/- 5.9 years. BMD was low at the femoral neck in 28.6% of patients and at the lumbar spine in 45.7%. Body mass index <= 30 kg/m(2) (adjusted odds ratio (OR) 3.43; 95% confidence interval (CI) 1.0-11.3) and postmenopausal status (OR adjusted 20.42; 95% CI 2.0-201.2) were associated with low BMD at the lumbar spine. Femoral neck measurements, age > 50 years (OR 3.41; 95% CI 1.0-11.6), and time since diagnosis > 50 months (OR adjusted 3.34; 95% CI 1.0-11.3) increased the likelihood of low BMD. Conclusion: These findings show that low BMD is common in middle-aged BCS. Factors were identified that may affect BMD in BCS and should be considered when implementing strategies to minimize bone loss in middle-aged women with breast cancer.

ABCtoolbox: a versatile toolkit for approximate Bayesian computations

Background The estimation of demographic parameters from genetic data often requires the computation of likelihoods. However, the likelihood function is computationally intractable for many realistic evolutionary models, and the use of Bayesian inference has therefore been limited to very simple models. The situation changed recently with the advent of Approximate Bayesian Computation (ABC) algorithms allowing one to obtain parameter posterior distributions based on simulations not requiring likelihood computations. Results Here we present ABCtoolbox, a series of open source programs to perform Approximate Bayesian Computations (ABC). It implements various ABC algorithms including rejection sampling, MCMC without likelihood, a Particle-based sampler and ABC-GLM. ABCtoolbox is bundled with, but not limited to, a program that allows parameter inference in a population genetics context and the simultaneous use of different types of markers with different ploidy levels. In addition, ABCtoolbox can also interact with most simulation and summary statistics computation programs. The usability of the ABCtoolbox is demonstrated by inferring the evolutionary history of two evolutionary lineages of Microtus arvalis. Using nuclear microsatellites and mitochondrial sequence data in the same estimation procedure enabled us to infer sex-specific population sizes and migration rates and to find that males show smaller population sizes but much higher levels of migration than females. Conclusion ABCtoolbox allows a user to perform all the necessary steps of a full ABC analysis, from parameter sampling from prior distributions, data simulations, computation of summary statistics, estimation of posterior distributions, model choice, validation of the estimation procedure, and visualization of the results.

Bayesian change-point analysis in linear regression model with scale mixtures of normal distributions

In this thesis, we consider Bayesian inference on the detection of variance change-point models with scale mixtures of normal (for short SMN) distributions. This class of distributions is symmetric and thick-tailed and includes as special cases: Gaussian, Student-t, contaminated normal, and slash distributions. The proposed models provide greater flexibility to analyze a lot of practical data, which often show heavy-tail and may not satisfy the normal assumption. As to the Bayesian analysis, we specify some prior distributions for the unknown parameters in the variance change-point models with the SMN distributions. Due to the complexity of the joint posterior distribution, we propose an efficient Gibbs-type with Metropolis- Hastings sampling algorithm for posterior Bayesian inference. Thereafter, following the idea of [1], we consider the problems of the single and multiple change-point detections. The performance of the proposed procedures is illustrated and analyzed by simulation studies. A real application to the closing price data of U.S. stock market has been analyzed for illustrative purposes.

Low bone mineral density, renal dysfunction, and fracture risk in HIV infection: a cross-sectional study

BACKGROUND: Reduced bone mineral density (BMD) is common in adults infected with human immunodeficiency virus (HIV). The role of proximal renal tubular dysfunction (PRTD) and alterations in bone metabolism in HIV-related low BMD are incompletely understood. METHODS: We quantified BMD (dual-energy x-ray absorptiometry), blood and urinary markers of bone metabolism and renal function, and risk factors for low BMD (hip or spine T score, -1 or less) in an ambulatory care setting. We determined factors associated with low BMD and calculated 10-year fracture risks using the World Health Organization FRAX equation. RESULTS: We studied 153 adults (98% men; median age, 48 years; median body mass index, 24.5; 67 [44%] were receiving tenofovir, 81 [53%] were receiving a boosted protease inhibitor [PI]). Sixty-five participants (42%) had low BMD, and 11 (7%) had PRTD. PI therapy was associated with low BMD in multivariable analysis (odds ratio, 2.69; 95% confidence interval, 1.09-6.63). Tenofovir use was associated with increased osteoblast and osteoclast activity (P< or = .002). The mean estimated 10-year risks were 1.2% for hip fracture and 5.4% for any major osteoporotic fracture. CONCLUSIONS: In this mostly male population, low BMD was significantly associated with PI therapy. Tenofovir recipients showed evidence of increased bone turnover. Measurement of BMD and estimation of fracture risk may be warranted in treated HIV-infected adults.

Toxics Release Inventory facilities and childhood cancer: Geographic information systems based approach

Purpose. To examine the association between living in proximity to Toxics Release Inventory (TRI) facilities and the incidence of childhood cancer in the State of Texas. ^ Design. This is a secondary data analysis utilizing the publicly available Toxics release inventory (TRI), maintained by the U.S. Environmental protection agency that lists the facilities that release any of the 650 TRI chemicals. Total childhood cancer cases and childhood cancer rate (age 0-14 years) by county, for the years 1995-2003 were used from the Texas cancer registry, available at the Texas department of State Health Services website. Setting: This study was limited to the children population of the State of Texas. ^ Method. Analysis was done using Stata version 9 and SPSS version 15.0. Satscan was used for geographical spatial clustering of childhood cancer cases based on county centroids using the Poisson clustering algorithm which adjusts for population density. Pictorial maps were created using MapInfo professional version 8.0. ^ Results. One hundred and twenty five counties had no TRI facilities in their region, while 129 facilities had at least one TRI facility. An increasing trend for number of facilities and total disposal was observed except for the highest category based on cancer rate quartiles. Linear regression analysis using log transformation for number of facilities and total disposal in predicting cancer rates was computed, however both these variables were not found to be significant predictors. Seven significant geographical spatial clusters of counties for high childhood cancer rates (p<0.05) were indicated. Binomial logistic regression by categorizing the cancer rate in to two groups (<=150 and >150) indicated an odds ratio of 1.58 (CI 1.127, 2.222) for the natural log of number of facilities. ^ Conclusion. We have used a unique methodology by combining GIS and spatial clustering techniques with existing statistical approaches in examining the association between living in proximity to TRI facilities and the incidence of childhood cancer in the State of Texas. Although a concrete association was not indicated, further studies are required examining specific TRI chemicals. Use of this information can enable the researchers and public to identify potential concerns, gain a better understanding of potential risks, and work with industry and government to reduce toxic chemical use, disposal or other releases and the risks associated with them. TRI data, in conjunction with other information, can be used as a starting point in evaluating exposures and risks. ^

A Bayesian approach to estimating the intraclass correlation coefficient

A Bayesian approach to estimating the intraclass correlation coefficient was used for this research project. The background of the intraclass correlation coefficient, a summary of its standard estimators, and a review of basic Bayesian terminology and methodology were presented. The conditional posterior density of the intraclass correlation coefficient was then derived and estimation procedures related to this derivation were shown in detail. Three examples of applications of the conditional posterior density to specific data sets were also included. Two sets of simulation experiments were performed to compare the mean and mode of the conditional posterior density of the intraclass correlation coefficient to more traditional estimators. Non-Bayesian methods of estimation used were: the methods of analysis of variance and maximum likelihood for balanced data; and the methods of MIVQUE (Minimum Variance Quadratic Unbiased Estimation) and maximum likelihood for unbalanced data. The overall conclusion of this research project was that Bayesian estimates of the intraclass correlation coefficient can be appropriate, useful and practical alternatives to traditional methods of estimation. ^

Searching for convergence in phylogenetic Markov chain Monte Carlo

Markov chain Monte Carlo (MCMC) is a methodology that is gaining widespread use in the phylogenetics community and is central to phylogenetic software packages such as MrBayes. An important issue for users of MCMC methods is how to select appropriate values for adjustable parameters such as the length of the Markov chain or chains, the sampling density, the proposal mechanism, and, if Metropolis-coupled MCMC is being used, the number of heated chains and their temperatures. Although some parameter settings have been examined in detail in the literature, others are frequently chosen with more regard to computational time or personal experience with other data sets. Such choices may lead to inadequate sampling of tree space or an inefficient use of computational resources. We performed a detailed study of convergence and mixing for 70 randomly selected, putatively orthologous protein sets with different sizes and taxonomic compositions. Replicated runs from multiple random starting points permit a more rigorous assessment of convergence, and we developed two novel statistics, delta and epsilon, for this purpose. Although likelihood values invariably stabilized quickly, adequate sampling of the posterior distribution of tree topologies took considerably longer. Our results suggest that multimodality is common for data sets with 30 or more taxa and that this results in slow convergence and mixing. However, we also found that the pragmatic approach of combining data from several short, replicated runs into a metachain to estimate bipartition posterior probabilities provided good approximations, and that such estimates were no worse in approximating a reference posterior distribution than those obtained using a single long run of the same length as the metachain. Precision appears to be best when heated Markov chains have low temperatures, whereas chains with high temperatures appear to sample trees with high posterior probabilities only rarely. [Bayesian phylogenetic inference; heating parameter; Markov chain Monte Carlo; replicated chains.]

Volumetric and areal bone mineral density measures are associated with cardiovascular disease in older men and women: The health, aging, and body composition study

The associations of volumetric (vBMD) and areal (aBMD) bone mineral density measures with prevalent cardiovascular disease (CVD) and subclinical peripheral arterial disease (PAD) were investigated in a cohort of older men and women enrolled in the Health, Aging, and Body Composition Study. Participants were 3,075 well-functioning white and black men and women (42% black, 51% women), aged 68-80 years. Total hip, femoral neck, and trochanter aBMD were measured using dual-energy X-ray absorptiometry. Quantitative computed tomography was used to evaluate spine trabecular, integral, and cortical vBMD measures in a subgroup (n = 1,489). Logistic regression was performed to examine associations of BMD measures with CVD and PAD. The prevalence of CVD (defined by coronary heart disease, PAD, cerebrovascular disease, or congestive heart failure) was 29.8%. Among participants without CVD, 10% had subclinical PAD (defined as ankle-arm index < 0.9). Spine vBMD measures were inversely associated with CVD in men (odds ratio of integral [ORintegral] = 1.34, 95% confidence interval [CI] 1.10-1.63; ORtrabecular = 1.25, 95% CI 1.02-1.53; ORcortical = 1.36, 95% CI 1.11-1.65). In women, for each standard deviation decrease in integral vBMD, cortical vBMD, or trochanter aBMD, the odds of CVD were significantly increased by 28%, 27%, and 22%, respectively. Total hip aBMD was associated with subclinical PAD in men (OR = 1.39, 95% CI 1.03-1.84) but not in women. All associations were independent of age and shared risk factors between BMD and CVD and were not influenced by inflammatory cytokines (interleukin-6 and tumor necrosis factors-alpha). In conclusion, our results provide further evidence for an inverse association between BMD and CVD in men and women. Future research should investigate common pathophysiological links for osteoporosis and CVD.

A Note on Bayesian Estimation for the Negative-Binomial Model

2000 Mathematics Subject Classification: 62F15.