Modeling correlated ordinal response data is usually more complex than the case of continuous and binary responses. Existing literature lacks an appropriate approach to modeling such data. For small sample sizes, however, these models lose their appeal since their inferences are based on large samples. In this work, the Bayesian analysis of an asymmetric bivariate ordinal latent variable model has been developed. The latent response variable has been chosen to follow the generalized bivariate Gumble distribution. Using some specific priors and MCMC algorithms the regression parameters were estimated. As an application, a data set concerning Diabetic Retinopathy in 116 patients have been analyzed. This data set includes the disease status of each eye for patients as an ordinal response and a number of explanatory variables some of which are common to both eyes and the rest are organ-specific.

In the survival analysis, when there is a cure fraction and the occurrence times of events are correlated, the cure frailty model is utilized. The main objective is to propose a method of analysis for two types of correlated frailty in the non-mixture cured model in order to separate the individual and shared heterogeneity between subjects. The cure models with correlated frailty and promotion time are considered. In both models, the likelihood function are based on piecewise exponential distribution for hazard function. To estimate the parameters, hierarchical Bayesian modeling is employed. Due to non-closed forms of the posteriors, they are estimated by MCMC algorithms. The Cox correlated frailty model is used as a benchmark and models are compared by DIC Criterion . The results show the superiority of cure models with correlated frailty.

Part of the recent literature on the evaluation of surrogate endpoints is started by a definition of validity in terms of both trial-level and individual-level association between a potential surrogate and a true endpoint. In another part, we review the main considerable statistical methods being proposed for the evaluation of a biomarker as surrogate endpoints, which have developed and consider how the validation process might be arranged within the regulatory and practical constraints evaluation. In the present work, we propose a new. Bayesian approach to evaluate individual level surrogacy. Deferent variations to prior distributions were implemented for responses with binomial distribution. Then these methods are compared in a simulation study. Finally, we apply and compare the previous and new methodology using a clinical study.

Sometimes it is impossible to directly measure the effect of intervention (medicine or therapeutic methods) in medical researches. That is because of high costs, long time, the aggressiveness of therapeutic methods, lack of clinical responses, and etc. In such cases, the effect of intervention on surrogate variables is measured. Many statistical studies have been accomplished for measuring the validity of surrogates and introducing a criterion for testing. The first criterion was established based on hypothesis testing. Other criterions were introduced over time. Then by using the classic methods, the Likelihood Ratio Factor was introduced. After that, the Bayesian Likelihood Ratio Factor developed and published. This article aims to introduce the Bayesian Likelihood Ratio Factor based on time dependent data. The illness under study is lung disease in victims of chemical weapons. The surrogate therapy method uses the forced expiratory volume at fist second.

In this paper the different types of autoregressive models were described for analysis of spatial data. Then the model parameters were estimated using maximum profile likelihood function by assuming that the dependent variables or error terms have spatially autoregressive relationship. Next all the models were evaluated and finally, the application of the model is illustrated in a real example.

The survival analysis methods are usually conducted based on assumption that the population is homogeneity. However, generally, this assumption in most cases is unrealistic, because of unobserved risk factors or subject specific random effect. Disregarding the heterogeneity leads to unbiased results. So frailty model as a mixed model was used to adjust for uncertainty that cannot be explained by observed factors in survival analysis. In this paper, family of power variance function distributions that includes gamma and inverse Gaussian distribution were introduced and evaluated for frailty effects. Finally the proportional hazard frailty models with Weibull baseline hazard as a parametric model used for analyzing survival data of the colorectal cancer patients.

Skew Normal distribution is important in analyzing non-normal data. The probability density function of skew Normal distribution contains integral function which tends researchers to some problems. Because of this problem, in this paper a simpler Bayesian approach using conditioning method is proposed to estimate the parameters of skew Normal distribution. Then the accuracy of this metrology is compared with ordinary Bayesian method in a simulation study.

One of the typical aims of statistical shape analysis, in addition to deriving an estimate of mean shape, is to get an estimate of shape variability. This aim is achived through employing the principal component analysis. Because the principal component analysis is limited to data on Euclidean space, this method cannot be applied for the shape data which are inherently non-Euclidean data. In this situation, the principal geodesic analysis or its linear approximation can be used as a generalization of the principal component analysis in non-Euclidean space. Because the main root of this method is the gradient descent algorithm, revealing some of its main defects, a new algorithm is proposed in this paper which leads to a robust estimate of mean shape and also preserves the geometrical structure of shape. Then, providing some theoretical aspects of principal geodesic analysis, its application is evaluated in a simulation study and in real data.

In Bayesian analysis of structured additive regression models which are a flexible class of statistical models, the posterior distributions are not available in a closed form, so Markov chain Monte Carlo algorithm due to complexity and large number of hyperparameters takes long time. Integrated nested Laplace approximation method can avoid the hard simulations using the Gaussian and Laplace approximations. In this paper, consideration of spatial correlation of the data in structured additive regression model and its estimation by the integrated nested Laplace approximation are studied. Then a crime data set in Tehran city are modeled and evaluated. Next, a simulation study is performed to compare the computational time and precision of the models provided by the integrated nested Laplace approximation and Markov chain Monte Carlo algorithm

In two level modeling, random effect and error's normality assumption is one of the basic assumptions. Violating this assumption leads to incorrect inference about coefficients of the model. In this paper, to resolve this problem, we use skew normal distribution instead of normal distribution for random and error components. Also, we show that ignoring positive (negative) skewness in the model causes overestimating (underestimating) in intercept estimation and underestimating (overestimating) in slope estimation by a simulation study. Finally, we use this model to study relationship between shift work and blood cholesterol.

Although the measurement error exists in the most scientific experiments, in order to simplify the modeling, its presence is usually ignored in statistical studying. In this paper, various approaches on estimating the parameters of multilevel models in presence of measurement error are studied. In addition, to improve the parameter estimates in this case, a new method is proposed which has high precision and reasonable convergence rate in compare with previous common approaches. Also, the performance of the proposed method as well as usual approaches are evaluated and compared using simulation study and analyzing real data of the income-expenditure of some households in Tehran city in 2008.

Bivariate Von Mises distribution, which behaves relatively similar to bivariate normal distributions, has been proposed for representing the simultaneously probabilistic variability of these angles. One of the remarkable properties of this distribution is having the univariate Von Mises as the conditional density. However, the marginal density takes various structures depend on its involved parameters and, in general, has no closed form. This issue encounters the statistical inference with particular problems. In this paper, this distribution and its properties are studied, then the procedure to sample via the acceptance-rejection algorithm is described. The problems encountered in choosing a proper candidate distribution, arising from the cyclic feature of both angles, is investigated and the properties of its conditional density is utilized to overcome this obstacle.

Recently, employing multivariate statistical techniques for data, that are geometrically random, made more attention by the researchers from applied disciplines. Shape statistics, as a new branch of stochastic geometry, constitute batch of such data. However, due to non-Euclidean feature of such data, adopting usual tools from the multivariate statistics to proper statistical analysis of them is not somewhat clear. How to cluster the shape data is studied in this paper and then its performance is compared with the traditional view of multivariate statistics to this subject via applying these methods to analysis the distal femur.

In this paper, we study the applicability of probabilistic solutions for the alignment of tertiary structure of proteins and discuss its difference with the deterministic algorithms. For this purpose, we introduce two Bayesian models and address a solution to add amino acid sequence and type (primary structure) to protein alignment. Furthermore, we will study the parameter estimation with Markov Chain Monte Carlo sampling from the posterior distribution. Finally, in order to see the effectiveness of these methods in the protein alignment, we have compared the parameter estimations in a real data set.