فصلنامه مدل سازی پیشرفته ریاضی
سال دوم شماره 2 (پاییز و زمستان 1391)

In the survival analysis with long term survivors، there are two classes of Models: Mixture Cure Model and Non-Mixture Cure Model. Whereas using the Mixture Cure model have some disadvantage such as uncertainly in identifiability of true parameter and when we use non informative uniform prior distribution for coefficient variation، the posterior distribution would be improper the Bayesian approach، we used the non-mixture cure model. Also there are a lot of immeasurable factors have effect on the survival probability then introduced the frailty in the survival analysis. In the non-mixture cure model Yin (2005) introduced the frailty. In this paper us insertion two definition of frailty and extend two new models. Also we show the better fitness of new models to Yin Models in the data set of leukemia. For estimation the parameter in these models we used the hierarchical Bayesian approach. We construction the likelihood functions based on piecewise exponential distribution and log-normal distribution for frailty distribution. Since the posteriors distribution do not have close form then we use the Markov Chain Monte Carlo methods. Based on the Deviance Information Criteria (DIC) the fitness on the proposal models confirmed.

In this paper، we consider and analyze several-step iterative methods for solving nonlinear equations.. This method is based on a direct Newtonian interpolation of the function and modified Adomian’s decomposition. We prove the important fact that methods obtained preserve their convergence order 3، without calculating any derivatives. Some numerical illustrations are given to show the efficiency of algorithms.

In spatial data analysis، the variogram function that determines the correlation structure is usually unknown، and most estimates based on observations. The presence of outliers affect on the estimation of the variogram function، trend parameters and spatial prediction. In this paper some new robust estimators of variogram are presented. The proposed estimators have highly breakdown points and are based on scale estimators. All proposed estimators are assessed based on simulation studies. In addition robust methods of trend estimation and spatial prediction are presented. Finally، a real world problem about the average temperature of 170 cities in Iran is analyzed using discussed methods.

The main subject of this paper is to consider the solution of singular perturbation problems which these problems appear in physical and engineering problems، such as fluid mechanics، chemical reactions، electronic circuitry، civil and fluid dynamics. In fact، a singular perturbation problem is in the form of either ordinary differential equations (O. D. E) or partial differential equations (P. D. E) in which the highest derivative is multiplied by some powers of as a positive small parameter. The purpose of the theory of singular perturbations is to solve a differential equation with some initial or boundary conditions with a small parameter. In this paper، the structure of solutions of these problems for second order ordinary differential equations with variable coefficients is considered. The next goal of this paper is to verify formation and non-formation of boundary layers in boundary points. Finally، the asymptotic expansions and uniform approximate solutions are obtained in five steps by using asymptotic matching condition.

Multilevel models provide suitable framework to study related data that are collected at various levels in many researches. In this paper، we propose a family of scale mixture of multivariate normal distributions for multilevel models. This family is more flexible than the normal distribution. The proposed model provides a better fit to the observed data in which their distribution has tails heavier than normal. The statistical inference of model parameters done by the marginal maximum likelihood leads to complex high-dimensional integrals and thus we implement the Markov chain Monte Carlo simulation approach for the Bayesian estimation of related parameters. In is shown that the kurtosis measure of different members in this family is different، therefore we fit multilevel models on a set of real data with imposing a variety of distributions in this family. Finally، by using the common model selection criteria we choose the best fitted model.

One efficient approach in classification is using a set of individual classifiers and then combining their outputs، usually knows as ensemble classification or multiple classifier system. In this paper، an ensemble classification system based on the random subspace approach is employed for diagnosis of endometriosis، in which individual classifiers of the ensemble system are trained with different feature subsets. Finally، for classifying an unknown test sample، classifiers’ outputs are fused using the majority voting combination rule.