Journal of Statistical Sciences

Constrained Bayes Estimators under Balanced Loss Functions

Ahmad Parsian

In this paper, a new class of estimators namely Constrained Bayes Estimators are obtained under Balanced Loss Function (BLF) and Weighted Balanced Loss Function (WBLF) using a ``Bayesian solution". The Constrained Bayes Estimators are calculated for the natural parameter of one-parameter exponential families of distributions. A common approach to the prior uncertainty in Bayesian analysis is to choose a class $Gamma$ of prior distributions and look for an optimal decision within the class $Gamma$. This is known as robust Bayesian methodology. Among several methods of choosing the optimal rules in the context of the robust Bayes method, we discuss obtaining Posterior Regret Constrained Gamma-Minimax (PRCGM) rule under Squared Error Loss and then employing the ``Bayesian solution", we obtain the optimal rules under BLF and WBLF.

Evaluation of Surrogate Endpoints by Bayesian Method

Soghrat Faghihzadeh

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.

Fitting Growth Regression Model to the Boolean Random Sets

Mojtaba Khazaei

One of the models that can be used to study the relationship between Boolean random sets and explanatory variables is growth regression model which is defined by generalization of Boolean model and permitting its grains distribution to be dependent on the values of explanatory variables. This model can be used in the study of behavior of Boolean random sets when their coverage regions variation is associated with the variation of grains size. In this paper we make possible the identification and fitting suitable growth model using available information in Boolean model realizations and values of explanatory variables. Also, a suitable method for fitting growth regression model is presented and properties of its obtained estimators are studied by a simulation study.

Hierarchical Bayesian Analysis of Cure Model with Correlated Frailty

Ebrahim Hajizadeh

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.

Power Comparisons of Goodness-of-Fit Tests Based on Entropy with Other Methods

Hadi Alizadeh Noughabi

In this paper we evaluate the power of the sample entropy goodness-of-fit tests for normal, exponential and uniform distributions and we compare them with the other statistical tests. We show, by simulation, that them have less power than of the other tests considered. We next introduce a new test for symmetry based on sample entropy and show, by simulation, that it has higher power than Cabilio and Masaro test (1996).

A Probability Problem in Distinct Fuzzy Subgroups of a Group

Hossein Naraghi

In this paper, first we define the commutativity of two fuzzy subgroups, and then we computed the probability of commutativity of the group Z_pⁿ which its support is exactly Z_p^mfor m<=n.