levent özbek
Ankara University, Statistics, Faculty Member
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This chapter is concerned with building a unified framework for concurrently generating data sets that include all four major kinds of variables (i.e., binary, ordinal, count, and normal) when the marginal distributions and a feasible... more
This chapter is concerned with building a unified framework for concurrently generating data sets that include all four major kinds of variables (i.e., binary, ordinal, count, and normal) when the marginal distributions and a feasible association structure are specified for simulation purposes. The simulation paradigm has been commonly employed in a wide spectrum of research fields including the physical, medical, social, and managerial sciences. A central aspect of every simulation study is the quantification of the model components and parameters that jointly define a scientific process. When this quantification cannot be performed via deterministic tools, researchers resort to random number generation (RNG) in finding simulation-based answers to address the stochastic nature of the problem. Although many RNG algorithms have appeared in the literature, a major limitation is that they were not designed to concurrently accommodate all variable types mentioned above. Thus, these algorithms provide only an incomplete solution, as real data sets include variables of different kinds. This work represents an important augmentation of the existing methods as it is a systematic attempt and comprehensive investigation for mixed data generation. We provide an algorithm that is designed for generating data of mixed marginals, illustrate its logistical, operational, and computational details; and present ideas on how it can be extended to span more complicated distributional settings in terms of a broader range of marginals and associational quantities.
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... Dosya Biçimi: PDF. Dil: Türkçe. Yazar(lar): ŞENOL, CEREN (Yazar),. Emeği Geçen(ler): ÖZBEK, LEVENT (Tez Danışmanı),. DOI: 10.1501/0003270. ... Linköping University, Technical Report No:1871, Sweden. Güler ., Kiymik MK, Akin M., Alkan... more
... Dosya Biçimi: PDF. Dil: Türkçe. Yazar(lar): ŞENOL, CEREN (Yazar),. Emeği Geçen(ler): ÖZBEK, LEVENT (Tez Danışmanı),. DOI: 10.1501/0003270. ... Linköping University, Technical Report No:1871, Sweden. Güler ., Kiymik MK, Akin M., Alkan A. 2001. ...
... Özbek, L., Özgen, F., Sütçigil, L., Aydın, H. 2004. Depresif ve normal deneklerin uyku EEG'leri arasındaki yapısal farklılıkların takura uzaklık ölçüsüyle degerlendirilmesi. ... Time series analysis univariate and multivariate... more
... Özbek, L., Özgen, F., Sütçigil, L., Aydın, H. 2004. Depresif ve normal deneklerin uyku EEG'leri arasındaki yapısal farklılıkların takura uzaklık ölçüsüyle degerlendirilmesi. ... Time series analysis univariate and multivariate methods. Addison-Wesley Publishing Company, Inc., USA. ...
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In this study, sleep electroencephalography (EEG) which is frequently used in statistical modelling has been modelled with the autoregressive (AR) time-series model and what kind of a structure the variance of the term white noise... more
In this study, sleep electroencephalography (EEG) which is frequently used in statistical modelling has been modelled with the autoregressive (AR) time-series model and what kind of a structure the variance of the term white noise included in the model represented in different sleep stages has been observed. Taking all of the stages scored in accordance with Rechtschaffen and Kales criterion into account separately, epoches in each stage have been modelled with the AR and the variance of the term white noise in this model has been monitored. The study has evaluated the sleep EEG variances of a subject. In accordance with the results, the heterogeneity at Stage 2 was thought to be the reason why the objective differences appeared in scoring. It is thought that this data pointed out a necessity that the period in Rechtschaffen and Kales scoring which is called Stage 2 must be revised.
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ABSTRACT The extended Kalman filter is extensively used in nonlinear state estimation problems. As long as the system characteristics are correctly known, the extended Kalman filter gives the best performance. However, when the system... more
ABSTRACT The extended Kalman filter is extensively used in nonlinear state estimation problems. As long as the system characteristics are correctly known, the extended Kalman filter gives the best performance. However, when the system information is partially known or incorrect, the extended Kalman filter may diverge or give biased estimates. An extensive number of works has been published to improve the performance of the extended Kalman filter. Many researchers have proposed the introduction of a forgetting factor, both into the Kalman filter and the extended Kalman filter, to improve the performance. However, there are 2 fundamental problems with this approach: the incorporation of the optimal forgetting factor into the (extended) Kalman filter and the selection of the optimal forgetting factor. These problems have not yet been fully resolved and are still open problems in the field. In this study, we propose a new adaptive fading extended Kalman filter with a matrix forgetting factor, and 2 methods are analyzed for the selection of the optimal forgetting factor. The stability properties of the proposed filter are also investigated. Results of the stability analysis show that the proposed filter is an exponential observer for nonlinear deterministic systems. Additionally, the convergence speed of the filter is simulated.
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In this study, the emergences of postsynaptic action potentials are investigated using simulation study which is depended on the statistical model of acetylcholine (Ach) quantal release theory at motor end-plate. It is supposed that the... more
In this study, the emergences of postsynaptic action potentials are investigated using simulation study which is depended on the statistical model of acetylcholine (Ach) quantal release theory at motor end-plate. It is supposed that the end-plate potentials (EPP) are sum of miniature end-plate potentials (MEPP) which are released as quantal and random in number (N). By the hypothesis that N number has a Poisson and MEPPs have a Gaussian distribution, EPPs are obtained by simulating distributions parameters. Our study suggests that the simulation of the EPPs are a convenient tool in understanding both physiological process of synaptic transmission and pathological process of neuromuscular junction.
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Bu calismada lineer regulator probleminde bulunan kayip fonksiyonunda bilinmeyen parametre olmasi durumunda bu parametrelerin en cok olabilirlik yontemiyle tahmini ele alinmistir. Bu amacla, ilk once durum-uzay modellerinde model... more
Bu calismada lineer regulator probleminde bulunan kayip fonksiyonunda bilinmeyen parametre olmasi durumunda bu parametrelerin en cok olabilirlik yontemiyle tahmini ele alinmistir. Bu amacla, ilk once durum-uzay modellerinde model parametrelerinin tahmini icin en cok olabilirlik yontemi, daha sonra lineer regulator problemi ve cozumu ile ilgili bilgi, son olarak kayip fonksiyonunda bulunan bilinmeyen parametrelerin en cok olabilirlik yontemiyle tahmini verilmistir. Simulasyon calismasi ile yontemin isleyisi gozlemlenmistir.
Kalman filtresi d inamik sistemlerde durum tahmin pro b leminin cozumu icin kullanilan populer bir tahmin yontemidir. Fen, muhendislik, ekonomi, askeri vb. olmak uzere bircok alandan probleme kolayca uygulanabilir. Sistem... more
Kalman filtresi d inamik sistemlerde durum tahmin pro b leminin cozumu icin kullanilan populer bir tahmin yontemidir. Fen, muhendislik, ekonomi, askeri vb. olmak uzere bircok alandan probleme kolayca uygulanabilir. Sistem karakteristikleri dogru olarak bilindigi surece Kalman filtresi en iyi tahmin performansi ile calisir. Ancak sistem karakteristiklerinin kismen bilindigi durumlarda veya yanlis bilindigi durumlarda filtrenin tahmin performansinda ciddi kayiplar olm asi kacinilmazdir. Kalman filtresin deki performans kaybi probl eminin ustesinden gelebilmek icin su ana kadar cok sayida calisma yayinlanmistir. Bir kisim arastirmaci tarafindan Sistem karakteristiklerinin kismen veya tamamen hatali bilinmesi durumunda, filtrelemede bazi guclendirmelerin yapilmasini saglayacak unutma faktoru ile uyarlanmis Kalman Filtresi tanitilmistir. “Adaptive estimation of multiple fading factors in Kalman filter for navigation applications” (AEMFFKF) bu calismalardan bir tanesidir. Bu calismada, co...
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... 11011115, 1987. [4] SL Campbell and WJ Terrell, Observability of linear time vary-ing descriptor systems, SIAM J. Matrix Anal. ... [5] SL Campbell, NK Nichols, and WJ Terrell, Duality, observability and controllability for linear... more
... 11011115, 1987. [4] SL Campbell and WJ Terrell, Observability of linear time vary-ing descriptor systems, SIAM J. Matrix Anal. ... [5] SL Campbell, NK Nichols, and WJ Terrell, Duality, observability and controllability for linear time-varying descriptor systems, Circuits, Syst. ...
Research Interests: Mechanical Engineering, Mathematics, Applied Mathematics, Computer Science, Statistics, and 10 moreConvergence, Estimation Theory, State Estimation, Kalman Filter, Measurement Errors, Convergence Rate, Electrical And Electronic Engineering, Central Limit Theorem, Asymptotic distribution, and State Space Model
Since the beginning of 2020, the world has been struggling with a viral epidemic (COVID-19), which poses a serious threat to the collective health of the human race. Mathematical modeling of epidemics is critical for developing such... more
Since the beginning of 2020, the world has been struggling with a viral epidemic (COVID-19), which poses a serious threat to the collective health of the human race. Mathematical modeling of epidemics is critical for developing such policies, especially during these uncertain times. In this study, the reproduction number and model parameters were predicted using AR(1) (autoregressive time-series model of order 1) and the adaptive Kalman filter (AKF). The data sample used in the study consists of the weekly and daily number of cases amongst the Ziraat Bank personnel between March 11, 2020, and April 19, 2021. This sample was modeled in the state space, and the AKF was used to estimate the number of cases per day. It is quite simple to model the daily and weekly case number time series with the time-varying parameter AR(1) stochastic process and to estimate the time-varying parameter with online AKF. Overall, we found that the weekly case number prediction was more accurate than the d...
This paper presents a two-compartment model for the transfer of opti- cal contrast agent, namely indocyanine green (ICG), in the presence of tumors between the plasma and extracellular extravascular space (EES) compartments. An adaptive... more
This paper presents a two-compartment model for the transfer of opti- cal contrast agent, namely indocyanine green (ICG), in the presence of tumors between the plasma and extracellular extravascular space (EES) compartments. An adaptive extended Kalman filter (EKF) has been derived to estimate the quantities that are transferred between the com- partments, Moreover, in order to validate the proposed EKF, real data have been utilized and the experimentally obtained ICG concentration data quantitatively analyzed through the estimation of physiological parameters related to capillary permeability and the optical contrast agent concentration in the compartments concurrently. The proposed method produces the estimate of tissue permeability, independent of the initial permeability values, without resorting to computationally expensive nonlinear fitting algorithms. Considering the fact that the change in the tissue permeability occurs usually due to a disease such as cancer, an estimated v...
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In this note, stability of the projection-based constrained discrete time extended Kalman filter (EKF) when applied to deterministic nonlinear systems has been studied. It is proved that, like the unconstrained case, under certain... more
In this note, stability of the projection-based constrained discrete time extended Kalman filter (EKF) when applied to deterministic nonlinear systems has been studied. It is proved that, like the unconstrained case, under certain assumptions, the EKF with state equality constraints is an exponential observer, i.e., it keeps the dynamics of its estimation error exponentially stable. Also, it has been shown
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In this note, stability of the projection-based constrained discrete time extended Kalman filter (EKF) when applied to deterministic nonlinear systems has been studied. It is proved that, like the unconstrained case, under certain... more
In this note, stability of the projection-based constrained discrete time extended Kalman filter (EKF) when applied to deterministic nonlinear systems has been studied. It is proved that, like the unconstrained case, under certain assumptions, the EKF with state equality constraints is an exponential observer, i.e., it keeps the dynamics of its estimation error exponentially stable. Also, it has been shown
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In this paper, the stability of the adaptive fading extended Kalman filter with the matrix forgetting factor when applied to the state estimation problem with noise terms in the non–linear discrete–time stochastic systems has been... more
In this paper, the stability of the adaptive fading extended Kalman filter with the matrix forgetting factor when applied to the state estimation problem with noise terms in the non–linear discrete–time stochastic systems has been analysed. The analysis is conducted in a similar manner to the standard extended Kalman filter’s stability analysis based on stochastic framework. The theoretical results show that under certain conditions on the initial estimation error and the noise terms, the estimation error remains bounded and the state estimation is stable.The importance of the theoretical results and the contribution to estimation performance of the adaptation method are demonstrated interactively with the standard extended Kalman filter in the simulation part.
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ABSTRACT This paper presents a two-compartment model for the transfer of opti-cal contrast agent, namely indocyanine green (ICG), in the presence of tumors between the plasma and extracellular extravascular space (EES) compartments. An... more
ABSTRACT This paper presents a two-compartment model for the transfer of opti-cal contrast agent, namely indocyanine green (ICG), in the presence of tumors between the plasma and extracellular extravascular space (EES) compartments. An adaptive extended Kalman filter (EKF) has been derived to estimate the quantities that are transferred between the com-partments, Moreover, in order to validate the proposed EKF, real data have been utilized and the experimentally obtained ICG concentration data quantitatively analyzed through the estimation of physiological parameters related to capillary permeability and the optical contrast agent concentration in the compartments concurrently. The proposed method produces the estimate of tissue permeability, independent of the initial permeability values, without resorting to computationally expensive nonlinear fitting algorithms. Considering the fact that the change in the tissue permeability occurs usually due to a disease such as cancer, an estimated value of the permeability could be used to extract valuable information about tumor cell behavior patterns.
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In this study, the estimation power of Extended Kalman Filter is tested within a simple Keynesian macroeconomic model. After the model is written in a non-linear state space form, Extended Kalman Filter emerges as the appropriate... more
In this study, the estimation power of Extended Kalman Filter is tested within a simple Keynesian macroeconomic model. After the model is written in a non-linear state space form, Extended Kalman Filter emerges as the appropriate methodology to estimate both state variables and the parameters. The simulation results suggest that such a methodology can also be employed in explaining more complex macroeconomic dynamics.
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The recent fluctuations in the oil prices have intensified the discussion on the dynamics and causes of real oil price changes. While the long-run component of real oil prices seems to have a stochastic trend, global real economic... more
The recent fluctuations in the oil prices have intensified the discussion on the dynamics and causes of real oil price changes. While the long-run component of real oil prices seems to have a stochastic trend, global real economic activity has been thought to generate important changes in real oil prices. Based on this argument, in this paper, we analyze the
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ABSTRACT In this paper the ingestion and subsequent metabolism of a drug in a given individual, are investigated through the use of compartmental models. An adaptive formulation of the widely used extended Kalman filter (EKF) has been... more
ABSTRACT In this paper the ingestion and subsequent metabolism of a drug in a given individual, are investigated through the use of compartmental models. An adaptive formulation of the widely used extended Kalman filter (EKF) has been derived in order to solve the resulting nonlinear estimation problem at the output of the compartments. The adaptive EKF employs a forgetting factor to emphasize artificially the effect of current data by exponentially weighting the observations. The dependence of EKF's performance on the selection of appropriate values of the arbitrary matrices, the measurement covariance R and the process noise covariance Q has been demonstrated through simulations. With the appropriate choice of the matrices the EKF provides a very useful tool for online estimation of both the state and the parameters.
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Ömürboyu gelir hipotezi mali politikaların Ricardo’cu denklik altında ömürboyu gelir üzerinde etkisi olmadığından hanehalkı tüketimini de etkileyemeyeceğini savunmaktadır. Ancak, Giavazzi ve Pagano (1990), Bertola ve Drazen (1993) ve... more
Ömürboyu gelir hipotezi mali politikaların Ricardo’cu denklik altında ömürboyu gelir üzerinde etkisi olmadığından hanehalkı tüketimini de etkileyemeyeceğini savunmaktadır. Ancak, Giavazzi ve Pagano (1990), Bertola ve Drazen (1993) ve Sutherland (1997)’ın mali stabilizasyon üzerine yaptıkları çalişmalar maliye politikalarının hanehalkı tüketimi üzerinde Keynesyen olarak nitelendirilen etkileri olduğunu göstermektedir. Bu etkilerin varlığı tüketici davranışlarının daha detaylı incelenmesine olanak sağladığı gibi, maliye politikalarının fiyat