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This paper presents a novel approach for analyzing bivariate positive data, taking into account a covariate vector and left-censored observations, by introducing a hierarchical Bayesian analysis. The proposed method assumes marginal Weibull distributions and employs either a usual Weibull likelihood or Weibull–Tobit likelihood approaches. A latent variable or frailty is included in the model to capture the possible correlation between the bivariate responses for the same sampling unit. The posterior summaries of interest are obtained through Markov Chain Monte Carlo methods. To demonstrate the effectiveness of the proposed methodology, we apply it to a bivariate data set from stellar astronomy that includes left-censored observations and covariates. Our results indicate that the new bivariate model approach, which incorporates the latent factor to capture the potential dependence between the two responses of interest, produces accurate inference results. We also compare the two models using the different likelihood approaches (Weibull or Weibull–Tobit likelihoods) in the application. Overall, our findings suggest that the proposed hierarchical Bayesian analysis is a promising approach for analyzing bivariate positive data with left-censored observations and covariate information. [ABSTRACT FROM AUTHOR]

The use of semiparametric or transformation models has been considered by many authors in the analysis of lifetime data in the presence of censoring and covariates as an alternative and generalization of the usual proportional hazards, the proportional odds models, and the accelerated failure time models, extensively used in lifetime data analysis. The inferences for the proportional hazards model introduced by Cox (1972) are usually obtained by maximum likelihood estimation methods assuming the partial likelihood function introduced by Cox (Cox, 1975). In this study, we consider a hierarchical Bayesian analysis of the proportional hazards model assuming the complete likelihood function obtained from a transformation model considering the unknown hazard function as a latent unknown variable under a Bayesian approach. Some applications with real time medical data illustrate the proposed methodology. [ABSTRACT FROM AUTHOR]

In the analysis of financial market data, random variations in price movements can share non-trivial statistical properties as observed for the distributions of returns, with possibility of absence of autocorrelations in asset returns, volatility in blocks and presence of asymmetry between rises and falls of stock values. Asset price fluctuations are usually investigated using time series models to obtain inferences about interest rates and future forecasts. In this study we consider the use of existing probability distributions to model run lengths and absolute historical price run returns as an alternative to the use of usual time series models with applications for time series obtained from the NYSE stock exchange for three private banks located in the Brazil in the period from July 19, 2013, to July 19, 2018. We assume discrete Weibull distributions as an alternative to the exponential law commonly used in this type of analysis. Under this modeling approach it is possible to obtain information about the structure of the market such as the probability of the stock market rising and falling daily and the magnitude of the returns. [ABSTRACT FROM AUTHOR]

In this paper, we order to evaluate via Monte Carlo simulations the performance of sample properties of the estimates of the estimates for Sushila distribution, introduced by Shanker et al. (2013). We consider estimates obtained by six estimation methods, the known approaches of maximum likelihood, moments and Bayesian method, and other less traditional methods: L-moments, ordinary least-squares and weighted least-squares. As a comparison criterion, the biases and the roots of mean-squared errors were used through nine scenarios with samples ranging from 30 to 300 (every 30rd). In addition, we also considered a simulation and a real data application to illustrate the applicability of the proposed estimators as well as the computation time to get the estimates. In this case, the Bayesian method was also considered. The aim of the study was to find an estimation method to be considered as a better alternative or at least interchangeable with the traditional maximum likelihood method considering small or large sample sizes and with low computational cost. [ABSTRACT FROM AUTHOR]

In this paper it is introduced a new two-parameter discrete distribution derived from the continuous Sushila distribution (Shanker et al., 2013). Its mathematical properties and estimation procedures for the parameters of the proposed model are presented assuming complete and right-censored data. This new model, in the same way as the continuous Sushila distribution, has the discrete Lindley distribution as a special case. An extensive simulation study is carried out to examine the bias and the roots of the mean squared errors for the maximum likelihood estimators as well the moments and Bayesian estimators of the proposed model parameters. Some examples using simulated data and real datasets are considered to show that the new proposed model performs at least as good as its particular case and some other traditional discrete models as the Poisson and geometric distributions. [ABSTRACT FROM AUTHOR]

The modeling and analysis of lifetime data in which the main endpoints are the times when an event of interest occurs is of great interest in medical studies. In these studies, it is common that two or more lifetimes associated with the same unit such as the times to deterioration levels or the times to reaction to a treatment in pairs of organs like lungs, kidneys, eyes or ears. In medical applications, it is also possible that a cure rate is present and needed to be modeled with lifetime data with long-term survivors. This paper presented a comparative study under a Bayesian approach among some existing continuous and discrete bivariate distributions such as the bivariate exponential distributions and the bivariate geometric distributions in presence of cure rate, censored data and covariates. In presence of lifetimes related to cured patients, it is assumed standard mixture cure rate models in the data analysis. The posterior summaries of interest are obtained using Markov Chain Monte Carlo methods. To illustrate the proposed methodology two real medical data sets are considered. [ABSTRACT FROM AUTHOR]

Time series models are often used in hydrology and meteorology studies to model streamflows series in order to make forecasting and generate synthetic series which are inputs for the analysis of complex water resources systems. In this paper we introduce a new modeling approach for hydrologic and meteorological time series assuming a continuous distribution for the data, where both the conditional mean and conditional variance parameters are modeled. Bayesian methods using standard MCMC (Markov Chain Monte Carlo Methods) are used to simulate samples for the joint posterior distribution of interest. Two applications to real data sets illustrate the proposed methodology, assuming that the observations come from a normal, a gamma or a beta distribution. A first example is given by a time series of monthly averages of natural streamflows, measured in the year period ranging from 1931 to 2010 in Furnas hydroelectric dam, Brazil. A second example is given with a time series of 313 air humidity data measured in a weather station of Rio Claro, a Brazilian city located in southeastern of Brazil. These applications motivate us to introduce new classes of models to analyze hydrological and meteorological time series. [ABSTRACT FROM AUTHOR]

In recent years, the use of copulas has grown rapidly, especially in survival analysis. In this paper, we introduce a bivariate modified Weibull distribu-tion derived from the Farlie{Gumbel{Morgenstern (FGM), a copula function commonly used to model very weak linear dependences. Considering the presence of non censored data and censored data, an extensive simulation study was developed to check the performance of the maximum likelihood method in estimating the parameters of the proposed model. Maximum like-lihood and Bayesian approaches for the estimation of the model parameters are presented. In the Bayesian analysis, the posterior distributions of the pa-rameters are estimated using Markov chain Monte Carlo (MCMC) method-ology. An example, considering a real data set, is introduced to illustrate the proposed methodology. [ABSTRACT FROM AUTHOR]

Some computational aspects to obtain classical and Bayesian inferences for the Basu and Dhar (1995) bivariate geometric distribution in presence of censored data and covariates are discussed in this paper. The posterior summaries of interest are obtained using standard existing MCMC (Markov Chain Monte Carlo) simulation methods available in popular free softwares as the OpenBugs software and the R software. Numerical illustrations are introduced considering simulated and real datasets showing that the use of discrete bivariate distributions may be a good alternative to the use of continuous bivariate distributions, in many areas of application. [ABSTRACT FROM AUTHOR]

Breast cancer is the second most common type of cancer in the world (World Cancer Report, 2014 a, b). The evolution of breast cancer treatment usually allows a longer life of patients as well in many cases a relapse of the disease. Usually medical researchers are interested to analyze data denoting the time until the occurrence of an event of interest such as the time of death by cancer in presence of right censored data and some covariates. In some situations, we could have two lifetimes associated to the same patient, as for example, the time free of the disease until recurrence and the total lifetime of the patient. In this case, it is important to assume a bivariate lifetime distribution which describes the possible dependence between the two observations. We consider as an application, different parametric bivariate lifetime distributions to analyze a breast cancer data set considering continuous or discrete data. Inferences of interest are obtained under a statistical Bayesian approach. We get the posterior summaries of interest using existing MCMC (Markov Chain Monte Carlo) methods. The main goal of the study, is to compare the bivariate continuous and discrete distributions that better describes the breast cancer lifetimes. [ABSTRACT FROM AUTHOR]

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In this paper a bivariate beta regression model with joint modeling of the mean and dispersion parameters is proposed, defining the bivariate beta distribution from Farlie–Gumbel–Morgenstern (FGM) copulas. This model, that can be generalized using other copulas, is a good alternative to analyze non-independent pairs of proportions and can be fitted applying standard Markov chain Monte Carlo methods. Results of two applications of the proposed model in the analysis of structural and real data set are included. [ABSTRACT FROM PUBLISHER]

In this paper we introduce a Bayesian analysis of a spherical distribution applied to rock joint orientation data in presence or not of a vector of covariates, where the response variable is given by the angle from the mean and the covariates are the components of the normal upwards vector. Standard simulation MCMC (Markov Chain Monte Carlo) methods have been used to obtain the posterior summaries of interest obtained from Win- Bugs software. Illustration of the proposed methodology are given using a simulated data set and a real rock spherical data set from a hydroelectrical site. [ABSTRACT FROM AUTHOR]

In this paper we develop a Bayesian analysis to estimate the disease prevalence, the sensitivity and specificity of three cervical cancer screening tests (cervical cytology, visual inspection with acetic acid and Hybrid Capture II) in the presence of a covariate and in the absence of a gold standard. We use Metropolis-Hastings algorithm to obtain the posterior summaries of interest. The estimated prevalence of cervical lesions was 6.4% (a 95% credible interval [95% CI] was 3.9, 9.3). The sensitivity of cervical cytology (with a result of ≥ ASC-US) was 53.6% (95% CI: 42.1, 65.0) compared with 52.9% (95% CI: 43.5, 62.5) for visual inspection with acetic acid and 90.3% (95% CI: 76.2, 98.7) for Hybrid Capture II (with result of >1 relative light units). The specificity of cervical cytology was 97.0% (95% CI: 95.5, 98.4) and the specificities for visual inspection with acetic acid and Hybrid Capture II were 93.0% (95% CI: 91.0, 94.7) and 88.7% (95% CI: 85.9, 91.4), respectively. The Bayesian model with covariates suggests that the sensitivity and the specificity of the visual inspection with acetic acid tend to increase as the age of the women increases. The Bayesian method proposed here is an useful alternative to estimate measures of performance of diagnostic tests in the presence of covariates and when a gold standard is not available. An advantage of the method is the fact that the number of parameters to be estimated is not limited by the number of observations, as it happens with several frequentist approaches. However, it is important to point out that the Bayesian analysis requires informative priors in order for the parameters to be identifiable. The method can be easily extended for the analysis of other medical data sets. [ABSTRACT FROM AUTHOR]

The performance of a diagnostic test is usually summarized by its sensitivity and specificity. Sensitivity is the probability of a positive result, once the individual is truly ill, and specificity is the probability of a negative result, regarding a healthy individual. These measures are obtained by comparing the test outcome and the results of a reference test generically denominated gold standard. However, in many applied problems considering two diagnostic tests, the gold standard is not available for those individuals with negative results on both tests. In addition, not all diagnostic tests have the same performance across different populations. In this context, we present a Bayesian inference approach for performance measures estimation and we propose an extension of this procedure involving the inclusion of covariates. This Bayesian approach is based on Markov Chain Monte Carlo methods. The conditional dependence between the diagnostic tests was considered. As an example, we applied the proposed methodology to a real data set obtained from the medical literature. [ABSTRACT FROM AUTHOR]

In this paper, we present a Bayesian analysis of exponential power mixture models in the presence of a covariate. Considering Gibbs sampling with MetropolisHastings algorithms, we obtain Monte Carlo estimates for the posterior quantities of interest. [ABSTRACT FROM AUTHOR]

Abstract: This paper presents estimates for the parameters included in long-term mixture and non-mixture lifetime models, applied to analyze survival data when some individuals may never experience the event of interest. We consider the case where the lifetime data have a two-parameters exponentiated exponential distribution. The two-parameter exponentiated exponential or the generalized exponential distribution is a particular member of the exponentiated Weibull distribution introduced by [31]. Classical and Bayesian procedures are used to get point and confidence intervals of the unknown parameters. We consider a general survival model where the scale, shape and cured fraction parameters of the exponentiated exponential distribution depends on covariates. [Copyright &y& Elsevier]

Abstract: In this paper, we introduce a Bayesian analysis for mixture of distributions belonging to the exponential family. As a special case we consider a mixture of normal exponential distributions including joint modeling of the mean and variance. We also consider joint modeling of the mean and variance heterogeneity. Markov Chain Monte Carlo (MCMC) methods are used to obtain the posterior summaries of interest. We also introduce and apply an EM algorithm, where the maximization is obtained applying the Fisher scoring algorithm. Finally, we also include analysis of real data sets to illustrate the proposed methodology. [Copyright &y& Elsevier]