İstatistik Bölümü Tez Koleksiyonu
http://hdl.handle.net/11655/300
2020-10-30T18:58:18ZBayesci grafik modelleri
http://hdl.handle.net/11655/22809
Bayesci grafik modelleri
Tuğrul, Özgür
Posterior distributions obtained by Bayesian approach usually have high dimensions when the models are rather complicated. Therefore, to reach the marjinal distributions from the models is analitically intractable. The aim of the study is to introduce the newest Bayesian practical techniques for the complicated models and to investigate Bayesian graphical model and Gibbs Sampling which is a Markov Chain Monte Carlo method together. BUGS package is used to show how the complicated models are solved iteratively. To understand the conditional structure of the models is very crucial for analysing the complicated models. Graphical models can be used to have a visual information of the structure of these models. Conditional independence allows us to factorize the joint distributions. Samples can be drawn iteratively from the marjinal distributions of the model parameters by Markov Chain Monte Carlo techniques. Then statistical inference can be make easier for the marjinal distiributions. Three different models are investigated in the study. BUGS package is used to have the visual representations of the three models. Gibbs samplings is applied for these models to obtain the marjinal distributions of the model parameters. The result obtained from Gibbs samplings are compared with the classical results in the multiple regression model. The changes in the number of iterations, initial values and the prior distributions of the models parameters are investigated. When the number of the iteration increases, the results are very close to true values. It is also seen in the study that the initial values are not so important if the number of iterations is high.
2001-01-01T00:00:00ZYİNELEMELİ SİNİR AĞLARI İLE FİNANSAL VERİ TAHMİNİ
http://hdl.handle.net/11655/22789
YİNELEMELİ SİNİR AĞLARI İLE FİNANSAL VERİ TAHMİNİ
KEÇECİ, EKİN
Recurrent Neural Network is an artificial neural network model which the outputs are re-included to network input in every iteration. The biggest advantage of recurrent neural networks is that they consider the variation of each sample in the sequential data depending on the previous examples. As reccurent neural network models developed, some theoretical obstacles emerged and different models were developed as solutions to these obstacles. It can be said that Long term short term memory (LSTM) networks are one of the most popular and best designed reccurent neural network models among these models. In this study, the success of LSTM model is compared to other neural network models in evaluating financial asset prices. The LSTM model gave better classification accuracy than other compared models.
2020-08-01T00:00:00ZÖLÇÜM HATALI AÇIKLAYICI DEĞİŞKENLİ COX REGRESYON MODELİNE BAYESCİ YAKLAŞIM
http://hdl.handle.net/11655/22748
ÖLÇÜM HATALI AÇIKLAYICI DEĞİŞKENLİ COX REGRESYON MODELİNE BAYESCİ YAKLAŞIM
Işık, Hatice
The Cox regression model with the measurement error covariate can cause an important bias when estimating coefficients by maximizing the known partial likelihood function. In this case, alternative estimation methods have been proposed and the effectiveness of these methods has been discussed. The measurement error occurs when the actual values of the covariates measured on a continuous scale cannot be obtained. Biological measurements such as systolic blood pressure and CD4 count, which are frequently used in survival analysis, are mostly variables with measurement error. The Bayesian approach is one of the methods used to reduce the bias arising from measurement error in the Cox regression model. In this thesis, the corrected Bayesian Cox regression model with polygonal prior to measurement error was proposed as an alternative to the partial likelihood function method, its Bayesian approach and the corrected Bayesian Cox regression model with Gamma prior to measurement error and its effectiveness was investigated.
The results of the Cox regression model obtained from the partial likelihood function, its Bayesian analysis, the corrected Bayesian Cox regression model with Gamma prior to measurement error, and the corrected Bayesian Cox regression model with polygonal prior to measurement error were compared. Simulation studies were performed with different scenarios to evaluate the performance of the estimators obtained with these methods. It is concluded that as a result of the analysis, in cases where the risk is high, the corrected Bayesian Cox regression model with Gamma prior to measurement error gives the best results in all scenarios, and in the case of low risk, not a suitable alternative in almost all scenarios. It is also shown that if the risk is low, the corrected Bayesian Cox regression model with polygonal prior to measurement error gives better results in low and medium reliability situations except for low censoring and large sample size, and at least one of the corrected models is an alternative method to Cox regression model and its Bayesian analysis in high reliability scenarios. However, if the model has the explanatory variable subject to measurement error, as the sample size increases, the coverage possibilities for the coefficients obtained by the classical method and its Bayesian analysis decrease well below the normal level especially in low and medium reliability cases.
To demonstrate the applicability of the methods in real data, the results of the primary biliary cirrhosis data from the Mayo Clinic study in R were obtained, compared, and interpreted. As a second application, model results were obtained for different samples randomly selected from AIDS data used by Goldman et al. (1996) in R. Based on the information obtained as a result of the simulation study, considering that the Cox and Bayesian Cox regression models are not suitable in the presence of measurement error covariate, the best model for both applications was obtained with the corrected Bayesian Cox regression model with polygonal prior to measurement error.
2020-01-01T00:00:00ZEliptik Konturlu Dağılımlara Dayalı Çok Değişkenli Tekrarlı Ölçümlü Varyans Analizi
http://hdl.handle.net/11655/22729
Eliptik Konturlu Dağılımlara Dayalı Çok Değişkenli Tekrarlı Ölçümlü Varyans Analizi
Borazan Çelikbıçak, Müge
Repeated measures data describe multiple measurements taken from the same experimental unit under different treatment conditions. In particular, researches with repeated measures data in various fields such as health and behavioral sciences, education, and psychology has an important role in applied statistics. The structure of dependency between different measurements taken from the same experimental unit appears as an issue that requires more attention in the analysis of repeated measures data and makes it more difficult than other statistical analyzes. There are many methods used to analyze the results of research designs planned with these measurements. The most important difference between these methods is the assumptions on which the models are based. By satisfying the assumptions that the models are based on among these methods, it is important to determine an appropriate method that can model the repeated measures data with the dependency structure. One of the most important assumptions needed by classical methods is the normality assumption. Many methods are valid under the assumption of normality. However, it is not always possible to hold this assumption in applications. For this reason, in the analysis of repeated measures data, different distributions are necessary that can provide flexibility beyond the normal distribution, especially in cases where the assumption of normality does not hold.
In this study, it is proposed to use the Multivariate Laplace distribution by examining the multivariate variance analysis model (MANOVA), which is a frequently used method for analysis of multivariate repeated measures data under Elliptically Contoured distributions, which is an alternative distribution family, in cases where normality assumption does not hold. Under this distribution assumption, the parameter estimates for the MANOVA model are carried out with the Maximum Likelihood method and, test statistics based on these estimators are proposed. The EM algorithm is used for parameter estimates based on the Maximum Likelihood method. In addition, the use of Matrix Variate Laplace distribution is proposed for the analysis of repeated measures data from nested designs under different treatment conditions, and model parameter estimates based on this distribution are made with the Maximum Likelihood estimation method. The Euclidean distances are calculated between the true parameter values and the estimates. Additionally, the power values are calculated for the test statistics.
2020-01-01T00:00:00Z