WInbugs

The paper deals with a Bayesian based Cox regression model to consider strategies for performing survivability of patients with breast cancer through Bayesian aspects. The proportional hazards model (PHM) in the context of survival data analysis, is same as Cox model and was introduced by Cox (1972) in order to estimate the effects of different covariates influencing the times-to-event data. It's well known that Bayesian analysis has the advantage in dealing with censored data and small sample over frequentist methods. Therefore, in this paper it deliberately explores the PHM for right-censored death times from Bayesian perspective, and compute the Bayesian estimator based on the Markov Chain Monte Carlo (MCMC) method. In particular it focuses on the approaches based on Gibbs sampler. Such approaches may be implemented using the publically available software BUGS. It aims to compare and apply Bayesian models of survivability for prediction of patients with breast cancer using outcome as explanatory variables and to produce better descriptions to survival of patients with breast cancer and of subgroups of patients with different survival characteristics.

In the presentation the method of small area estimation under spatial Simultaneous Autoregressive (SAR) model is presented. The estimation was conducted using both spatial EBLUP and hierarchical Bayes method with SAR random effects that depend on proximity matrix and spatial autoregression coefficient (rho). The presentation continues the idea of small area estimation by means of hierarchical Bayes method in the case of known model hyperparameters, presented in a previous work of one of the authors. The computations performed by sae package for R-project environment and special procedure prepared for WinBUGS software reveal that consistent estimates (for point estimates, for measures of variability - such as estimation error and for random effects) can be obtained. As an example the data on average per capita available income from Polish Household Budget Survey for counties (NUTS4) and auxiliary variables from Polish Tax Register (POLTAX) were used together with digital maps for Polish counties. The precision estimation for direct estimates were obtained by means of three-stage method, where Balanced Repeated Replication (BRR), bootstrap and Generalized Variance Function were used. The results of the computations reveal that for higher values of rho some MSE reduction can be observed. This effect for HB-SAR method is even more evident than for common spatial EBLUP. The computations done with Gibbs sampler also demonstrate simultaneous nature of simulated processes especially for random effects. In our opinion, the Gibbs sampler can be a good starting point for other computation methods that seems more adequate for this kind of stochastic processes.

The author presents a method of hierarchical bayesian estimation to estimate the value of the different income variables on the basis of studies of household budgets and POLTAX tax register. Calculations have been made for the case where approximately known a priori evaluation of hyperparameters used to construct a conditional probability, which is used in the model. The author compares the efficiency of the estimates obtained by using other hierarchical methods of estimation for small areas, including the EBLUP estimators type. This gave congruity in precision of the estimated parameters using both techniques.

Ce document est le premier chapitre de mon cours "Statistique Bayésienne" pour les étudiants de la 3iéme année de l'ESSAI (Université de Carthage). On introduit quelques notions de base de la Statistique Bayésienne. Je finis ce chapitre par une utilisation des modèles bayésiens Multinomiales pour la prédication des élections présidentielles 2016 aux US.

Freeway crash occurrences are highly influenced by geometric characteristics, traffic status, weather conditions and drivers' behavior. For a mountainous freeway which suffers from adverse weather conditions, it is critical to incorporate real-time weather information and traffic data in the crash frequency study. In this paper, a Bayesian inference method was employed to model one year's crash data on I-70 in the state of Colorado. Real-time weather and traffic variables, along with geometric characteristics variables were evaluated in the models. Two scenarios were considered in this study, one seasonal and one crash type based case. For the methodology part, the Poisson model and two random effect models with a Bayesian inference method were employed and compared in this study. Deviance Information Criterion (DIC) was utilized as a comparison factor. The correlated random effect models outperformed the others. The results indicate that the weather condition variables, especially precipitation, play a key role in the crash occurrence models. The conclusions imply that different active traffic management strategies should be designed based on seasons, and single-vehicle crashes have different crash mechanism compared to multi-vehicle crashes.

While rural freeways generally have lower crash rates, interactions between driver behavior, traffic and geometric characteristics, and adverse weather conditions may increase the crash risk along some freeway sections. This paper examines the safety effects of roadway geometrics on crash occurrence along a freeway section that features mountainous terrain and adverse weather. Starting from preliminary exploration using Poisson models, Bayesian hierarchical models with spatial and random effects were developed to efficiently model the crash frequencies on road segments on the 20-mile freeway section of study. Crash data for 6 years (2000–2005), roadway geometry, traffic characteristics and weather information in addition to the effect of steep slopes and adverse weather of snow and dry seasons, were used in the investigation. Estimation of the model coefficients indicates that roadway geometry is significantly associated with crash risk; segments with steep downgrades were found to drastically increase the crash risk. Moreover, this crash risk could be significantly increased during snow season compared to dry season as a confounding effect between grades and pavement condition. Moreover, sites with higher degree of curvature, wider medians and an increase of the number of lanes appear to be associated with lower crash rate. Finally, a Bayesian ranking technique was implemented to rank the hazard levels of the roadway segments; the results confirmed that segments with steep downgrades are more crash prone along the study section.

In the paper the method of parameters estimation using hierarchical Bayes (HB) method in the case of known model hyperparameters for a priori conditionals was presented. This approach has some advantage in comparison with subjective model parameters selection because of more simulation stability and allows obtaining estimates that has more regular distribution. As an example the data about average per capita income from Polish Household Budget Survey for counties (NUTS4) and auxiliary variables from Polish Tax Register (POLTAX) were used. The computation was done using WinBUGS software and R-project environment with R2WinBUGS package, which control the simulations in WinBUGS, and coda package, which allows performing the analysis of simulation results. In the paper sample code in R-project that can be used as a pattern for further similar applications was also presented. The efficiency of hierarchical Bayes estimation with other small area methods was compared. Such comparison was d...

In the presentation the method of parameters estimation using hierarchical Bayes (HB) method in the case of known model hyperparameters for a priori conditionals was presented. This approach has some advantage in comparison with subjective model parameters selection because of more simulation stability and allows obtaining estimates that has more regular distribution. As an example the data about average per capita income from Polish Household Budget Survey for counties (NUTS4) and auxiliary variables from Polish Tax Register (POLTAX) were used. The computation was done using WinBUGS software and R-project environment with R2WinBUGS package, which control the simulations in WinBUGS, and coda package, which allows performing the analysis of simulation results. In the paper sample code in R-project that can be used as a pattern for further similar applications was also presented. The efficiency of hierarchical Bayes estimation with other small area methods was compared. Such comparison was done for HB and EBLUP techniques, for which some consistency related to the precision of estimates obtained using both techniques was achieved.

The aim of this paper is to investigate the association between material deprivation index and
relative risk of infant mortality for 81 administrative districts in Peninsular Malaysia. This
investigation is essential for the regional planning and development by policy makers in order
to identify and conduct possible efforts to reduce the socioeconomic inequality and health
disparities across the different regions in the country. We begin this investigation by
developing index of material deprivation based on several indicators available from census
data and expected value of infant mortality based on the number of infant mortality and live
birth for each administrative district using the administrative registration data of the years
1991 and 2000. Since Bayesian hierarchical modeling is flexible as it allows the idea of
“borrowing information”, we apply the technique to estimate the expected values of material
deprivation index and relative risk of infant mortality for each individual administrative
district. Association between material deprivation and relative risk of infant mortality is
studied based on the two measures found using graphical methods involving caterpillar charts
and superimposition of choropleth maps. In addition, Pearson product moment correlation is
computed to determine the overall association. The graphical methods indicate that there exist
some tendency where some districts which experienced high relative risk of infant mortality
also observed high index of material deprivation and vice versa. The overall results showed
that there are moderate positive correlations between material deprivation and relative risk of
infant mortality for the years 1991 and 2000, as given by the values of correlation coefficient
values of 0.48 and 0.45 respectively, indicating no significant temporal change over the two
periods.

Survival analysis is a collection of statistical techniques which examine the time it takes for an event to occur, and it is one of the most important fields in biomedical sciences and other variety of scientific disciplines. Furthermore, the computational rapid advancements in recent decades have advocated the application of Bayesian techniques in this field, giving a powerful and flexible alternative to the classical inference. e aim of this study is to consider the Bayesian inference for the generalized log-logistic proportional hazard model with applications to right-censored healthcare data sets. We assume an independent gamma prior for the baseline hazard parameters and a normal prior is placed on the regression coefficients. We then obtain the exact form of the joint posterior distribution of the regression coefficients and distributional parameters. e Bayesian estimates of the parameters of the proposed model are obtained using the Markov chain Monte Carlo (McMC) simulation technique. All computations are performed in Bayesian analysis using Gibbs sampling (BUGS) syntax that can be run with Just Another Gibbs Sampling (JAGS) from the R software. A detailed simulation study was used to assess the performance of the proposed parametric proportional hazard model. Two real-survival data problems in the healthcare are analyzed for illustration of the proposed model and for model comparison. Furthermore, the convergence diagnostic tests are presented and analyzed. Finally, our research found that the proposed parametric proportional hazard model performs well and could be beneficial in analyzing various types of survival data.