Thesis (Ph. D.)--Florida State University, 2004. / Advisor: Dr. Joseph Pignatiello, Jr., Florida State University, College of Engineering, Dept. of Industrial Engineering. Title and description from dissertation home page (viewed Sept. 23, 2004). Includes bibliographical references.

Thesis (M. Sc.)--University of Canterbury, 2008. / Typescript (photocopy). "8 February 2008." Includes bibliographical references (p. 112-114). Also available via the World Wide Web.

Thesis (M.A.S.)--Memorial University of Newfoundland, 2004. / Restricted until October 2005. Bibliography: leaves 92-100.

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Literature on change point analysis mostly requires a sudden change in the data distribution, either in a few parameters or the distribution as a whole. We are interested in the scenario that the variance of data may make a significant jump while the mean of data changes in a smooth fashion. It is motivated by a liver procurement experiment with organ surface temperature monitoring. Blindly applying the existing change point analysis methods to the example can yield erratic change point estimates since the smoothly-changing mean violates the sudden-change assumption. In my dissertation, we propose a penalized weighted least squares approach with an iterative estimation procedure that naturally integrates variance change point detection and smooth mean function estimation. Given the variance components, the mean function is estimated by smoothing splines as the minimizer of the penalized weighted least squares. Given the mean function, we propose a likelihood ratio test statistic for identifying the variance change point. The null distribution of the test statistic is derived together with the rates of convergence of all the parameter estimates. Simulations show excellent performance of the proposed method. Application analysis offers numerical support to the non-invasive organ viability assessment by surface temperature monitoring. The method above can only yield the variance change point of temperature at a single point on the surface of the organ at a time. In practice, an organ is often transplanted as a whole or in part. Therefore, it is generally of more interest to study the variance change point for a chunk of organ. With this motivation, we extend our method to study variance change point for a chunk of the organ surface. Now the variances become functions on a 2D space of locations (longitude and latitude) and the mean is a function on a 3D space of location and time. We model the variance functions by thin-plate splines and the mean function by the tensor product of thin-plate splines and cubic splines. However, the additional dimensions in these functions incur serious computational problems since the sample size, as a product of the number of locations and the number of sampling time points, becomes too large to run the standard multi-dimensional spline models. To overcome the computational hurdle, we introduce a multi-stages subsampling strategy into our modified iterative algorithm. The strategy involves several down-sampling or subsampling steps educated by preliminary statistical measures. We carry out extensive simulations to show that the new method can efficiently cut down the computational cost and make a practically unsolvable problem solvable with reasonable time and satisfactory parameter estimates. Application of the new method to the liver surface temperature monitoring data shows its effectiveness in providing accurate status change information for a portion of or the whole organ. / Ph. D.

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Evidence of networks in the resting-brain reflecting the spontaneous brain activity is perhaps the most significant discovery to understand intrinsic brain functionality. Moreover, subsequent detection of dynamics in these networks can be milestone in differentiating the normal and disordered brain functions. However, capturing the correct dynamics is a challenging task since no ground truths' are present for comparison of the results. The change points of these networks can be different for different subjects even during normal brain functions. Even for the same subject and session, dynamics can be different at the start and end of the session based on the fatigue level of the subject scanned. Despite the absence of ground truths, studies have analyzed these dynamics using the existing methods and some of them have developed new algorithms too. One of the most commonly used method for this purpose is sliding window correlation. However, the result of the sliding window correlation is dependent on many parameters and without the ground truth there is no way of validating the results. In addition, most of the new algorithms are complicated, computationally expensive, and/or focus on just one aspect on these dynamics. This study applies the algorithms and concepts from signal processing, image processing, video processing, information theory, and machine learning to analyze the results of the sliding window correlation and develops a novel algorithm to detect change points of these networks adaptively. The findings in this study are divided into three parts: 1) Analyzing the extent of variability in well-defined networks of rodents and humans with sliding window correlation applying concepts from information theory and machine learning domains. 2) Analyzing the performance of sliding window correlation using simulated networks as ground truths for best parameters’ selection, and exploring its dependence on multiple frequency components of the correlating signals by processing the signals in time and Fourier domains. 3) Development of a novel algorithm based on image similarity measures from image and video processing that maybe employed to identify change points of these networks adaptively.

Thesis (MScEng)--Stellenbosch University, 2012. / ENGLISH ABSTRACT: In this research work, auto-associative neural networks have been used for changepoint detection. This is a nonlinear technique that employs the use of artificial neural networks as inspired among other by Frank Rosenblatt’s linear perceptron algorithm for classification. An auto-associative neural network was used successfully to detect change-points for various types of time series data. Its performance was compared to that of singular spectrum analysis developed by Moskvina and Zhigljavsky. Fraction of Explained Variance (FEV) was also used to compare the performance of the two methods. FEV indicators are similar to the eigenvalues of the covariance matrix in principal component analysis. Two types of time series data were used for change-point detection: Gaussian data series and nonlinear reaction data series. The Gaussian data had four series with different types of change-points, namely a change in the mean value of the time series (T1), a change in the variance of the time series (T2), a change in the autocorrelation of the time series (T3), and a change in the crosscorrelation of two time series (T4). Both linear and nonlinear methods were able to detect the changes for T1, T2 and T4. None of them could detect the changes in T3. With the Gaussian data series, linear singular spectrum analysis (LSSA) performed as well as the NLSSA for the change point detection. This is because the time series was linear and the nonlinearity of the NLSSA was therefore not important. LSSA did even better than NLSSA when comparing FEV values, since it is not subject to suboptimal solutions as could sometimes be the case with autoassociative neural networks. The nonlinear data consisted of the Belousov-Zhabotinsky (BZ) reactions, autocatalytic reaction time series data and data representing a predator-prey system. With the NLSSA methods, change points could be detected accurately in all three systems, while LSSA only managed to detect the change-point on the BZ reactions and the predator-prey system. The NLSSA method also fared better than the LSSA method when comparing FEV values for the BZ reactions. The LSSA method was able to model the autocatalytic reactions fairly accurately, being able to explain 99% of the variance in the data with one component only. NLSSA with two nodes on the bottleneck attained an FEV of 87%. The performance of both NLSSA and LSSA were comparable for the predator-prey system, both systems, where both could attain FEV values of 92% with a single component. An auto-associative neural network is a good technique for change point detection in nonlinear time series data. However, it offers no advantage over linear techniques when the time series data are linear. / AFRIKAANSE OPSOMMING: In hierdie navorsing is outoassosiatiewe neurale netwerk gebruik vir veranderingspuntwaarneming. Dis is ‘n nielineêre tegniek wat neurale netwerke gebruik soos onder andere geïnspireer deur Frank Rosnblatt se lineêre perseptronalgoritme vir klassifikasie. ‘n Outoassosiatiewe neurale netwerk is suksesvol gebruik om veranderingspunte op te spoor in verskeie tipes tydreeksdata. Die prestasie van die outoassosiatiewe neurale netwerk is vergelyk met singuliere spektrale oontleding soos ontwikkel deur Moskvina en Zhigljavsky. Die fraksie van die verklaarde variansie (FEV) is ook gebruik om die prestasie van die twee metodes te vergelyk. FEV indikatore is soortgelyk aan die eiewaardes van die kovariansiematriks in hoofkomponentontleding. Twee tipes tydreeksdata is gebruik vir veranderingspuntopsporing: Gaussiaanse tydreekse en nielineêre reaksiedatareekse. Die Gaussiaanse data het vier reekse gehad met verskillende veranderingspunte, naamlik ‘n verandering in die gemiddelde van die tydreeksdata (T1), ‘n verandering in die variansie van die tydreeksdata (T2), ‘n verandering in die outokorrelasie van die tydreeksdata (T3), en ‘n verandering in die kruiskorrelasie van twee tydreekse (T4). Beide lineêre en nielineêre metodes kon die veranderinge in T1, T2 en T4 opspoor. Nie een het egter daarin geslaag om die verandering in T3 op te spoor nie. Met die Gaussiaanse tydreeks het lineêre singuliere spektrumanalise (LSSA) net so goed gevaar soos die outoassosiatiewe neurale netwerk of nielineêre singuliere spektrumanalise (NLSSA), aangesien die tydreekse lineêr was en die vermoë van die NLSSA metode om nielineêre gedrag te identifiseer dus nie belangrik was nie. Inteendeel, die LSSA metode het ‘n groter FEV waarde getoon as die NLSSA metode, omdat LSSA ook nie blootgestel is aan suboptimale oplossings, soos wat soms die geval kan wees met die afrigting van die outoassosiatiewe neural netwerk nie. Die nielineêre data het bestaan uit die Belousov-Zhabotinsky (BZ) reaksiedata, ‘n outokatalitiese reaksietydreeksdata en data wat ‘n roofdier-prooistelsel verteenwoordig het. Met die NLSSA metode kon veranderingspunte betroubaar opgespoor word in al drie tydreekse, terwyl die LSSA metode net die veranderingspuntin die BZ reaksie en die roofdier-prooistelsel kon opspoor. Die NLSSA metode het ook beter gevaaar as die LSSA metode wanneer die FEV waardes vir die BZ reaksies vergelyk word. Die LSSA metode kon die outokatalitiese reaksies redelik akkuraat modelleer, en kon met slegs een komponent 99% van die variansie in die data verklaar. Die NLSSA metode, met twee nodes in sy bottelneklaag, kon ‘n FEV waarde van slegs 87% behaal. Die prestasie van beide metodes was vergelykbaar vir die roofdier-prooidata, met beide wat FEV waardes van 92% kon behaal met hulle een komponent. ‘n Outoassosiatiewe neural netwerk is ‘n goeie metode vir die opspoor van veranderingspunte in nielineêre tydreeksdata. Dit hou egter geen voordeel in wanneer die data lineêr is nie.

Cette thèse est consacrée à l'étude de modèles de Lévy exponentiels en finance, et en particulier : 1. aux propriétés de continuité de prix d'options en fonction des paramètres de processus de Lévy, 2. à la préservation de la propriété de Lévy lors du passage à une mesure martingale de f-divergence minimale, 3. à l'étude de modèles de type change-point, obtenus par recollement à un instant aléatoire de deux exponentielles de processus de Lévy. Pour l'étude de la continuité, on obtient d'abord des résultats de convergence pour les processus de Lévy sous les mesures martingales et on en déduit par la factorisation de Wiener-Hopf la convergence de nombreux prix d'options. On donne ensuite des résultats de continuité de prix sous différentes mesures martingales minimisant des f-divergences. Il a été remarqué que la préservation de la propriété de Lévy a lieu pour toute f-divergence dont la dérivée seconde est une fonction puissante. On montre que sous certaines conditions sur les paramètres des processus de Lévy, la préservation n'a lieu que pour des f-divergences classiques. La dualité entre maximisation d'utilité et minimisation de f-divergence nous permet alors d'obtenir une formule générale pour certaines stratégies optimales. Pour les modèles de type change-point, on décrit la forme des mesures martingales de f-divergence minimale en explicitant le lien avec les mesures minimales associés aux deux processus de Lévy sous-jacents. On donne également la forme de stratégies optimales liées à la maximisation d'utilité.