Sequential Bayesian modeling of non-stationary non-Gaussian processes
| dc.contributor | Ph.D. Program in Electrical and Electronic Engineering. | |
| dc.contributor.advisor | Ertüzün, Ayşın. | |
| dc.contributor.advisor | Kuruoğlu, Ercan E. | |
| dc.contributor.author | Gençağa, Orhan Deniz. | |
| dc.date.accessioned | 2023-03-16T10:24:59Z | |
| dc.date.available | 2023-03-16T10:24:59Z | |
| dc.date.issued | 2007. | |
| dc.description.abstract | This thesis brings a unifying approach for modeling non-stationary non-Gaussian signals which are widely encountered in many multidisciplinary research fields. In the literature, different approaches have been used to model non-stationary signals. However, they could not fulfill the increasing needs where non-Gaussian processes are involved until the development of Sequential Monte Carlo techniques (particle filters). In general particle filtering, the problem is expressed in terms of nonlinear and/or non-Gaussian state-space equations and we need information about the functional form of the state variations. In this thesis, we bring a general solution for cases where these variations are unknown and the process distributions cannot be expressed by a closed form probability density function. We propose a novel modeling scheme which is as unified as possible to cover these problems. First, a novel technique is proposed to model Time-Varying Autoregressive Alpha Stable processes where unknown, time-varying autoregressive coefficients and distribution parameters can be estimated. Successful performances have been supported by posterior Cramer Rao Lower Bound values. Next, we extend our methodology to model cross-correlated signals where vector autoregressive processes with non-Gaussian driving signals can also be modeled. Later, this extension is used as a building block to provide a more unifying solution where both mixing matrix and latent processes are modeled from their mixtures. This can be interpreted as a solution for non-stationary Dependent Component Analysis. Successful simulation results verify that our methodology is very flexible and provides a unifying solution for the modeling of non-stationary processes in all cases described above. | |
| dc.format.extent | 30cm. | |
| dc.format.pages | xxiii, 190 leaves; | |
| dc.identifier.other | EE 2007 G46 PhD | |
| dc.identifier.uri | https://digitalarchive.library.bogazici.edu.tr/handle/123456789/13079 | |
| dc.publisher | Thesis (Ph.D.)-Bogazici University. Institute for Graduate Studies in Science and Engineering, 2007. | |
| dc.relation | Includes appendices. | |
| dc.relation | Includes appendices. | |
| dc.subject.lcsh | Gaussian processes. | |
| dc.subject.lcsh | Bayesian statistical decision theory. | |
| dc.title | Sequential Bayesian modeling of non-stationary non-Gaussian processes |
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