Özlem Türkşen

Statistical inference for geometric process with the inverse Gaussian distribution

In this study, the statistical inference problem for the geometric process (GP) is considered when the distribution of the first occurrence time is assumed to be inverse Gaussian (IG). The parameters a, μ and of the GP are estimated by using the maximum likelihood (ML) method, where a, μ and are the ratio of the GP, the mean and the variance of the IG distribution, respectively. Asymptotic distributions and consistency properties of the ML estimators are obtained. These asymptotic distributions enable us to give a test statistic which distinguishes a renewal process from a geometric process. Monte Carlo simulations are performed to compare the efficiencies of the ML estimators with the widely used nonparametric modified moment (MM) estimators. It is seen from the results that the ML estimators are more efficient than the MM estimators. Further, three real-life examples are given for application purposes.

Comparison of multi-objective algorithms applied to feature selection

The feature selection problem can be formulated as a multi-objective optimization (MOO) problem, as it involves the minimization of the feature subset cardinality and the misclassification error. In this chapter, a comparison of MOO algorithms applied to feature selection is presented. The used MOO methods are: Nondominated Sorting Genetic Algorithm II (NSGA-II), Archived Multi Objective Simulated Annealing (AMOSA), and Direct Multi Search (DMS). To test the feature subset solutions, Takagi- Sugeno fuzzy models are used as classifiers. To solve the feature selection problem, AMOSA was adapted to deal with discrete optimization. The multi-objective methods are applied to four benchmark datasets used in the literature and the obtained results are compared and discussed.

Statistical inference for α-series process with the inverse Gaussian distribution

ABSTRACT Statistical inferences for the geometric process (GP) are derived when the distribution of the first occurrence time is assumed to be inverse Gaussian (IG). An α-series process, as a possible alternative to the GP, is introduced since the GP is sometimes inappropriate to apply some reliability and scheduling problems. In this study, statistical inference problem for the α-series process is considered where the distribution of first occurrence time is IG. The estimators of the parameters α, μ, and σ2 are obtained by using the maximum likelihood (ML) method. Asymptotic distributions and consistency properties of the ML estimators are derived. In order to compare the efficiencies of the ML estimators with the widely used nonparametric modified moment (MM) estimators, Monte Carlo simulations are performed. The results showed that the ML estimators are more efficient than the MM estimators. Moreover, two real life datasets are given for application purposes.

Comparison of fuzzy logic based models for the multi-response surface problems with replicated response measures

Multi-response problems with replicated response measures are considered.Fuzzy least squares regression (FLSR) and fuzzy clustering based modeling methods, switching fuzzy C-regression (SFCR) and Takagi-Sugeno (TS) fuzzy model, were used for modeling of multi-response experiment data with replicated response measures.In this paper, the SFCR is used for the first time to model the replicated response measured data sets.It was seen that the SFCR had the better prediction performance rather than FLSR and TS fuzzy model according to the root mean square error (RMSE). A replicated multi-response experiment is a process that includes more than one responses with replications. One of the main objectives in these experiments is to estimate the unknown relationship between responses and input variables simultaneously. In general, classical regression analysis is used for modeling of the responses. However, in most practical problems, the assumptions for regression analysis cannot be satisfied. In this case, alternative modeling methods such as fuzzy logic based modeling approaches can be used. In this study, fuzzy least squares regression (FLSR) and fuzzy clustering based modeling methods, which are switching fuzzy C-regression (SFCR) and Takagi-Sugeno (TS) fuzzy model, are preferred. The novelty of the study is presenting the applicability of SFCR to the multi-response experiment data set with replicated response measures. Three real data set examples are given for application purposes. In order to compare the prediction performance of modeling approaches, root mean square error (RMSE) criteria is used. It is seen from the results that the SFCR gives the better prediction performance among the other fuzzy modeling approaches for the replicated multi-response experimental data sets.

Statistical Inference for Two-Compartment Model Parameters with Bootstrap Method and Genetic Algorithm

Two-compartment model has common usage in modeling stage of dynamical systems. It is possible to consider the two-compartment model as a regression model which is intrinsically nonlinear in parameters. Evaluation of the nonlinear model parameters in statistical perspective will help to improve the compartmental system. In this study, statistical inference of two-compartment model parameters is achieved in respect to point estimation and interval estimation. The point estimates of compartment model parameters are obtained according to the nonlinear least squares (NLS) approach. Genetic algorithm (GA), a well-known population-based evolutionary algorithm, is preferred as an optimization tool. The main contribution of the study is obtaining bias-corrected point estimates and bias-corrected accelerated confidence interval (CI) estimates of compartment parameters. In order to obtain the CIs, sampling distribution of parameter estimates is defined with the application of fixed-X nonlinear bootstrap method which preserves the fixed nature of predictor variable. Two bootstrap methods are used for CI calculations: (i) Percentile and (ii) bias-corrected accelerated (BCa). A simulated data set and a real data set from the pharmacokinetic (PK) literature are chosen for application purpose. It is seen from the results that bias-reduced point estimates and sampling distribution of parameter estimates can be obtained by preserving the time-dependent nature of the dynamical system by using fixed-X bootstrapping. Besides, BCa method gives more realistic interval estimates than percentile method.

Parameter Estimation of Nonlinear Response Surface Models by Using Genetic Algorithm and Unscented Kalman Filter

Some of the real world problems are characterized by using nonlinear functions in the parameters. In this case, optimization of nonlinear response surface models become challenging with derivative-based optimization methods. In this study, two of the derivative free methods, Genetic Algorithm (GA) and Unscented Kalman Filter (UKF), are used for parameter estimation of complex nonlinear response surface model. A numerical example in chemical science is given to illustrate the performance of the methods.

Bulanık Çok Yanıtlı Deneyler İçin Bulanık Pareto Çözüm Kümesinin Bulanık İlişkiye Dayalı Sınıflandırma Yaklaşımı İle Değerlendirilmesi

The solution set of a multi-response experiment is characterized by Pareto solution set. In this paper, the multiresponse experiment is dealed in a fuzzy framework. The responses and model parameters are considered as triangular fuzzy numbers which indicate the uncertainty of the data set. Fuzzy least square approach and fuzzy modified NSGA-II (FNSGA-II) are used for modeling and optimization, respectively. The obtained fuzzy Pareto solution set is grouped by using fuzzy relational clustering approach. Therefore, it could be easier to choose the alternative solutions to make better decision. A fuzzy response valued real data set is used as an application.