京都大学 / 新制・課程博士 / 博士(情報学) / 甲第25423号 / 情博第861号 / 新制||情||144(附属図書館) / 京都大学大学院情報学研究科知能情報学専攻 / (主査)特定教授 黒橋 禎夫, 教授 河原 達也, 教授 西野 恒 / 学位規則第4条第1項該当 / Doctor of Informatics / Kyoto University / DFAM

Neste trabalho de tese propomos um modelo de regressão beta com erros de medida. Esta proposta é uma área inexplorada em modelos não lineares na presença de erros de medição. Abordamos metodologias de estimação, como máxima verossimilhança aproximada, máxima pseudo-verossimilhança aproximada e calibração da regressão. O método de máxima verossimilhança aproximada determina as estimativas maximizando diretamente o logaritmo da função de verossimilhança. O método de máxima pseudo-verossimilhança aproximada é utilizado quando a inferência em um determinado modelo envolve apenas alguns mas não todos os parâmetros. Nesse sentido, dizemos que o modelo apresenta parâmetros de interesse como também de perturbação. Quando substituímos a verdadeira covariável (variável não observada) por uma estimativa da esperança condicional da variável não observada dada a observada, o método é conhecido como calibração da regressão. Comparamos as metodologias de estimação mediante um estudo de simulação de Monte Carlo. Este estudo de simulação evidenciou que os métodos de máxima verossimilhança aproximada e máxima pseudo-verossimilhança aproximada tiveram melhor desempenho frente aos métodos de calibração da regressão e naïve (ingênuo). Utilizamos a linguagem de programação Ox (Doornik, 2011) como suporte computacional. Encontramos a distribuição assintótica dos estimadores, com o objetivo de calcular intervalos de confiança e testar hipóteses, tal como propõem Carroll et. al.(2006, Seção A.6.6), Guolo (2011) e Gong e Samaniego (1981). Ademais, são utilizadas as estatísticas da razão de verossimilhanças e gradiente para testar hipóteses. Num estudo de simulação realizado, avaliamos o desempenho dos testes da razão de verossimilhanças e gradiente. Desenvolvemos técnicas de diagnóstico para o modelo de regressão beta com erros de medida. Propomos o resíduo ponderado padronizado tal como definem Espinheira (2008) com o objetivo de verificar as suposições assumidas ao modelo e detectar pontos aberrantes. Medidas de influência global, tais como a distância de Cook generalizada e o afastamento da verossimilhança, são utilizadas para detectar pontos influentes. Além disso, utilizamos a técnica de influência local conformal sob três esquemas de perturbação (ponderação de casos, perturbação da variável resposta e perturbação da covariável com e sem erros de medida). Aplicamos nossos resultados a dois conjuntos de dados reais para exemplificar a teoria desenvolvida. Finalmente, apresentamos algumas conclusões e possíveis trabalhos futuros. / In this thesis, we propose a beta regression model with measurement error. Among nonlinear models with measurement error, such a model has not been studied extensively. Here, we discuss estimation methods such as maximum likelihood, pseudo-maximum likelihood, and regression calibration methods. The maximum likelihood method estimates parameters by directly maximizing the logarithm of the likelihood function. The pseudo-maximum likelihood method is used when the inference in a given model involves only some but not all parameters. Hence, we say that the model under study presents parameters of interest, as well as nuisance parameters. When we replace the true covariate (observed variable) with conditional estimates of the unobserved variable given the observed variable, the method is known as regression calibration. We compare the aforementioned estimation methods through a Monte Carlo simulation study. This simulation study shows that maximum likelihood and pseudo-maximum likelihood methods perform better than the calibration regression method and the naïve approach. We use the programming language Ox (Doornik, 2011) as a computational tool. We calculate the asymptotic distribution of estimators in order to calculate confidence intervals and test hypotheses, as proposed by Carroll et. al (2006, Section A.6.6), Guolo (2011) and Gong and Samaniego (1981). Moreover, we use the likelihood ratio and gradient statistics to test hypotheses. We carry out a simulation study to evaluate the performance of the likelihood ratio and gradient tests. We develop diagnostic tests for the beta regression model with measurement error. We propose weighted standardized residuals as defined by Espinheira (2008) to verify the assumptions made for the model and to detect outliers. The measures of global influence, such as the generalized Cook\'s distance and likelihood distance, are used to detect influential points. In addition, we use the conformal approach for evaluating local influence for three perturbation schemes: case-weight perturbation, respose variable perturbation, and perturbation in the covariate with and without measurement error. We apply our results to two sets of real data to illustrate the theory developed. Finally, we present our conclusions and possible future work.

Neste trabalho de tese propomos um modelo de regressão beta com erros de medida. Esta proposta é uma área inexplorada em modelos não lineares na presença de erros de medição. Abordamos metodologias de estimação, como máxima verossimilhança aproximada, máxima pseudo-verossimilhança aproximada e calibração da regressão. O método de máxima verossimilhança aproximada determina as estimativas maximizando diretamente o logaritmo da função de verossimilhança. O método de máxima pseudo-verossimilhança aproximada é utilizado quando a inferência em um determinado modelo envolve apenas alguns mas não todos os parâmetros. Nesse sentido, dizemos que o modelo apresenta parâmetros de interesse como também de perturbação. Quando substituímos a verdadeira covariável (variável não observada) por uma estimativa da esperança condicional da variável não observada dada a observada, o método é conhecido como calibração da regressão. Comparamos as metodologias de estimação mediante um estudo de simulação de Monte Carlo. Este estudo de simulação evidenciou que os métodos de máxima verossimilhança aproximada e máxima pseudo-verossimilhança aproximada tiveram melhor desempenho frente aos métodos de calibração da regressão e naïve (ingênuo). Utilizamos a linguagem de programação Ox (Doornik, 2011) como suporte computacional. Encontramos a distribuição assintótica dos estimadores, com o objetivo de calcular intervalos de confiança e testar hipóteses, tal como propõem Carroll et. al.(2006, Seção A.6.6), Guolo (2011) e Gong e Samaniego (1981). Ademais, são utilizadas as estatísticas da razão de verossimilhanças e gradiente para testar hipóteses. Num estudo de simulação realizado, avaliamos o desempenho dos testes da razão de verossimilhanças e gradiente. Desenvolvemos técnicas de diagnóstico para o modelo de regressão beta com erros de medida. Propomos o resíduo ponderado padronizado tal como definem Espinheira (2008) com o objetivo de verificar as suposições assumidas ao modelo e detectar pontos aberrantes. Medidas de influência global, tais como a distância de Cook generalizada e o afastamento da verossimilhança, são utilizadas para detectar pontos influentes. Além disso, utilizamos a técnica de influência local conformal sob três esquemas de perturbação (ponderação de casos, perturbação da variável resposta e perturbação da covariável com e sem erros de medida). Aplicamos nossos resultados a dois conjuntos de dados reais para exemplificar a teoria desenvolvida. Finalmente, apresentamos algumas conclusões e possíveis trabalhos futuros. / In this thesis, we propose a beta regression model with measurement error. Among nonlinear models with measurement error, such a model has not been studied extensively. Here, we discuss estimation methods such as maximum likelihood, pseudo-maximum likelihood, and regression calibration methods. The maximum likelihood method estimates parameters by directly maximizing the logarithm of the likelihood function. The pseudo-maximum likelihood method is used when the inference in a given model involves only some but not all parameters. Hence, we say that the model under study presents parameters of interest, as well as nuisance parameters. When we replace the true covariate (observed variable) with conditional estimates of the unobserved variable given the observed variable, the method is known as regression calibration. We compare the aforementioned estimation methods through a Monte Carlo simulation study. This simulation study shows that maximum likelihood and pseudo-maximum likelihood methods perform better than the calibration regression method and the naïve approach. We use the programming language Ox (Doornik, 2011) as a computational tool. We calculate the asymptotic distribution of estimators in order to calculate confidence intervals and test hypotheses, as proposed by Carroll et. al (2006, Section A.6.6), Guolo (2011) and Gong and Samaniego (1981). Moreover, we use the likelihood ratio and gradient statistics to test hypotheses. We carry out a simulation study to evaluate the performance of the likelihood ratio and gradient tests. We develop diagnostic tests for the beta regression model with measurement error. We propose weighted standardized residuals as defined by Espinheira (2008) to verify the assumptions made for the model and to detect outliers. The measures of global influence, such as the generalized Cook\'s distance and likelihood distance, are used to detect influential points. In addition, we use the conformal approach for evaluating local influence for three perturbation schemes: case-weight perturbation, respose variable perturbation, and perturbation in the covariate with and without measurement error. We apply our results to two sets of real data to illustrate the theory developed. Finally, we present our conclusions and possible future work.

The estimation of latent variable models with ordinal and continuous, or ranking variables is the research focus of this thesis. The existing estimation methods are discussed and a composite likelihood approach is developed. The main advantages of the new method are its low computational complexity which remains unchanged regardless of the model size, and that it yields an asymptotically unbiased, consistent, and normally distributed estimator. The thesis consists of four papers. The first one investigates the two main formulations of the unrestricted Thurstonian model for ranking data along with the corresponding identification constraints. It is found that the extra identifications constraints required in one of them lead to unreliable estimates unless the constraints coincide with the true values of the fixed parameters. In the second paper, a pairwise likelihood (PL) estimation is developed for factor analysis models with ordinal variables. The performance of PL is studied in terms of bias and mean squared error (MSE) and compared with that of the conventional estimation methods via a simulation study and through some real data examples. It is found that the PL estimates and standard errors have very small bias and MSE both decreasing with the sample size, and that the method is competitive to the conventional ones. The results of the first two papers lead to the next one where PL estimation is adjusted to the unrestricted Thurstonian ranking model. As before, the performance of the proposed approach is studied through a simulation study with respect to relative bias and relative MSE and in comparison with the conventional estimation methods. The conclusions are similar to those of the second paper. The last paper extends the PL estimation to the whole structural equation modeling framework where data may include both ordinal and continuous variables as well as covariates. The approach is demonstrated through an example run in R software. The code used has been incorporated in the R package lavaan (version 0.5-11).

Hintergrund. Exzessives Sorgen ist durch anhaltende, sich wiederholende negative Gedanken gekennzeichnet, die als aufdringlich und unkontrollierbar empfunden werden. Chronisches Sorgen kann zu einer schwer beeinträchtigenden mentalen Aktivität werden und es wird angenommen, dass es zur Entstehung, Aufrechterhaltung und Verschlechterung einer Reihe von somatischen Gesundheitsproblemen und psychischen Störungen beiträgt. Theoretische Modelle und empirische Befunde deuten darauf hin, dass exzessives Sorgen mit einer gestörten Bottom-up-Salienzverarbeitung, einer unzureichenden Top-down-Aufmerksamkeitssteuerung, Defiziten in der Emotionsregulation und abnormalen selbstreferenziellen mentalen Funktionen verbunden sind. Neuroimaging-Studien zu exzessivem Sorgen zeigen Veränderungen funktioneller Aktivierung und Konnektivität in limbischen und paralimbischen Hirnstrukturen, welche die Reaktivität auf emotionale Stimuli unterstützen, in präfrontalen Strukturen, die in Top-down-Prozesse involviert sind, welche der Aufmerksamkeitssteuerung und Emotionsregulation zugrunde liegen, und in medialen kortikalen Mittellinienstrukturen, die an selbstreferenziellen mentalen Aktivitäten beteiligt sind. Im Hinblick auf das Vorhandensein, die genaue Lokalisation der beteiligten Hirnareale und die Richtung der Effekte präsentieren diese Studien jedoch weitgehend heterogene Ergebnisse. Die hohe Variabilität der Befunde erschwert es, ein kohärentes Verständnis der neurobiologischen Mechanismen exzessiven Sorgens zu erlangen. Um dieses Verständnis zu erweitern und künftige Richtungen für die weitere Forschung auf diesem Gebiet aufzuzeigen, verfolgte die vorliegende Dissertationsschrift drei Ziele: (i) die emotionsbezogene, aufgabenbasierte fMRT-Literatur zu exzessivem Sorgen auf quantitative, datengesteuerte Weise zusammenzufassen, um konsistente funktionelle Störungen über Studien hinweg zu identifizieren; (ii) zu bestimmen, mit welchen psychologischen Prozessen die identifizierten Hirnregionen assoziiert sind, und in welchen funktionellen Hirnnetzwerken sie wirken; und (iii) Anomalien in der grundlegenden Hirnorganisation zu untersuchen, die mit exzessivem Sorgen assoziiert sind. Methoden. Eine State-of-the-Art koordinatenbasierte Meta-Analyse wurde unter Anwendung des Activation Likelihood Estimation (ALE) Algorithmus durchgeführt, um die Übereinstimmung zwischen 16 Neuroimaging-Experimenten zu bestimmen, die Veränderungen in der funktionellen Aktivität des Gehirns während der Verarbeitung emotionaler Inhalte zwischen Personen mit hoher und normaler Sorgenneigung berichten. Die identifizierten Regionen wurden mithilfe von Metadaten der funktionellen Magnetresonanztomographie (fMRT) hinsichtlich ihrer psychologischen Funktionen charakterisiert (Verhaltens-Charakterisierung). Zusätzlich wurde meta-analytic-connectivity modeling (MACM) verwendet, um ihre globalen funktionellen Konnektivitätsmuster zu bestimmen und so zugehörige Gehirnnetzwerke zu identifizieren. Schließlich wurde fMRT im Ruhezustand (resting-state) verwendet, um die funktionellen Konnektivitätsmuster zwischen 21 Personen mit hoher und 21 Personen mit normaler Sorgenneigung ohne einer aufgabenbezogenen Gehirnaktivierung zu vergleichen. Dispositionelle Sorgen wurden mit dem Penn State Worry Questionnaire als verlässliches Selbstauskunftsmaß für schwere Sorgen erhoben. Saatregion-basierte Analysen mit den meta-analytisch abgeleiteten Hirnregionen als Saatregionen und eine datengesteuerte Multi-Voxel-Pattern-Analyse (MVPA) wurden durchgeführt, um funktionelle Konnektivitätsunterschiede zwischen den beiden Gruppen zu detektieren. Darüber hinaus wurden gruppenüber-greifende Korrelationen zwischen dem aktuellen Sorgenausmaß (State-Sorgen) und den funktionellen Konnektivitätsmustern der Saat-Regionen sowie den aus der MVPA abgeleiteten Komponenten-Werten analysiert. Ergebnisse. Die Meta-Analyse ergab konvergente Anomalien bei Individuen mit hoher im Vergleich mit normaler Sorgenneigung, hauptsächlich in einem linkshemisphärischen Cluster, welcher Teile des mittleren frontalen Gyrus, des inferioren frontalen Gyrus und der anterioren Insula umfasst. Die Verhaltens-Charakterisierung zeigte, dass der identifizierte Cluster mit der Sprachverarbeitung und dem Gedächtnis assoziiert ist. Darüber hinaus ergaben die meta-analytischen Konnektivitätskartierungen starke funktionelle Verbindungen zwischen den beobachteten konvergenten Regionen und frontalen, temporalen und parietalen Hirnregionen, die sich mit Teilen von zwei verhaltensrelevanten Hirnnetzwerken überschneiden, nämlich dem Salienznetzwerk (SN) und dem Default-Netzwerk (DN). Die resting-state funktionellen Konnektivitätsanalysen zeigten keine Unterschiede zwischen Individuen mit hoher und normaler Sorgenneigung und auch keine Korrelationen zwischen den resting-state funktionellen Konnektivitätsmustern und State-Sorgen, weder mit dem auf Saatregionen basierenden Ansatz noch mit dem MVPA-Ansatz. Schlussfolgerungen. Die Ergebnisse dieser Dissertationsschrift deuten darauf hin, dass exzessives Sorgen mit einer gestörten Funktion in Hirnarealen zusammenhängt, die mit bottom-up und top-down Aufmerksamkeitssteuerung sowie Emotionserzeugung und Emotionsregulation in Verbindung gebracht werden. Die Verhaltensanalyse deckte Assoziationen zwischen dem identifizierten Cluster und der Sprachverarbeitung auf, die mit dem übermäßigen inneren Sprechen bei zu Sorgen neigenden Personen zusammenhängen könnten. Diese Assoziation ist bisher eher unbeachtet geblieben und sollte weiter erforscht werden. Darüber hinaus stellen die identifizierten Hirnregionen Schlüsselknoten in interagierenden neuronalen Netzwerken dar, die endogen und exogen orientierte Kognition unterstützen und das dynamische Zusammenspiel zwischen diesen Prozessen steuern. Ihre veränderte netzwerkübergreifende Dynamik könnte die Ursache für die Unfähigkeit von zu schweren Sorgen neigen-den Personen sein, sich von intern orientierten Kognitionen zu lösen, wenn adaptives Reagieren einen externen Fokus der Aufmerksamkeit erfordern würde. Die Nullergebnisse der Ruhezustandsanalysen könnten auf das Studiendesign zurückzuführen sein oder durch Charakteristika des Sorgens selbst verursacht werden, werden aber nicht als Beleg dafür interpretiert, dass Anomalien in der intrinsischen Konnektivität des Gehirns in Verbindung mit exzessivem Sorgen nicht vorhanden sind. Die Ergebnisse dieser Arbeit können zukünftige Forschungen anleiten, die z.B. untersuchen könnten, ob und wie sich die dynamischen zeitlichen Interaktionen innerhalb und zwischen den hier identifizierten Netzwerken in Abhängigkeit vom Schweregrad des Sorgens unterscheiden. Die ALE-Ergebnisse liefern eine A-priori-Auswahl von Hirnregionen für solche Studien. Ein besseres Verständnis der Veränderungen in den Gehirnnetzwerken, die exzessivem Sorgen zugrunde liegen, und der psychologischen Funktionen, die dadurch beeinträchtigt werden, wird Ansatzpunkte für die Verbesserung therapeutischer Interventionen liefern.:Contents TABLES VIII FIGURES IX ABBREVIATIONS X ABSTRACT 1 1 THEORETICAL BACKGROUND 6 1.1 WORRY 6 1.1.1 DEFINITION, NATURE AND FUNCTION OF WORRY 6 1.1.2 THE WORRY CONTINUUM – NORMAL VERSUS MALADAPTIVE WORRY 7 1.1.3 THE DELETERIOUS EFFECTS OF EXCESSIVE WORRY 8 1.1.4 THEORETICAL MODELS OF EXCESSIVE WORRY 11 1.2 FUNCTIONAL BRAIN NETWORKS AND EXCESSIVE WORRY 18 1.2.1 A SYSTEMS NEUROSCIENCE VIEW OF EXCESSIVE WORRY 18 1.2.2 EMPIRICAL EVIDENCE: FMRI STUDIES ON EXCESSIVE WORRY 20 1.3 RESEARCH QUESTION 32 2 STUDY I: A QUANTITATIVE META-ANALYSIS OF FMRI STUDIES INVESTIGATING EMOTIONAL PROCESSING IN EXCESSIVE WORRIERS: APPLICATION OF ACTIVATION LIKELIHOOD ESTIMATION ANALYSIS 35 2.1 ABSTRACT 36 2.2 INTRODUCTION 37 2.3 METHODS 40 2.3.1 LITERATURE SEARCH AND STUDY SELECTION 40 2.3.2 ACTIVATION LIKELIHOOD ESTIMATION 46 2.3.3 META-ANALYTIC CONNECTIVITY MODELING 47 2.3.4 ANALYSIS OF BEHAVIORAL DOMAIN PROFILES 47 2.4 RESULTS 48 2.4.1 SIGNIFICANT ALE CLUSTERS 48 2.4.2 FUNCTIONAL CONNECTIVITY OF THE DERIVED ALE-CLUSTER – MACM-ANALYSIS 51 2.4.3 FUNCTIONAL CHARACTERIZATION OF THE DERIVED ALE-CLUSTER – BEHAVIORAL ANALYSIS 54 2.5 DISCUSSION 55 2.6 CONCLUSION 59 2.7 SUPPLEMENTARY MATERIAL STUDY I: LISTING OF ALE CLUSTERS SIGNIFICANT AT P < 0.001 UNCORRECTED, CLUSTER SIZE > 100MM3 60 3 STUDY II: HIGH AND LOW WORRIERS DO NOT DIFFER IN UNSTIMULATED RESTING-STATE BRAIN CONNECTIVITY 61 3.1 ABSTRACT 62 3.2 INTRODUCTION 63 3.3 MATERIALS AND METHODS 65 3.3.1 PARTICIPANTS AND PROCEDURE 65 3.3.2 FMRI DATA ACQUISITION 66 3.3.3 SELF-REPORT ASSESSMENTS AND STATE WORRY ASSESSMENT 66 3.3.4 STATISTICAL ANALYSES 67 3.4 RESULTS 69 3.4.1 SELF-REPORT MEASURES 69 3.4.2 FMRI RESULTS 72 3.5 DISCUSSION 72 3.6 CONCLUSION 75 3.7 SUPPLEMENTARY MATERIAL STUDY II: STATE WORRY ASSESSMENT 75 4 GENERAL DISCUSSION 76 4.1 CONVERGENT ABERRANT FUNCTION IN THE MFG-IFG-INSULA-CLUSTER 76 4.2 META-ANALYTIC FUNCTIONAL CHARACTERIZATION AND CONNECTIVITY MAPPING OF THE MFG-IFG-INSULA CLUSTER 82 4.3 NO RESTING-STATE FUNCTIONAL CONNECTIVITY DIFFERENCES BETWEEN HW AND LW 84 4.4 STRENGTHS AND LIMITATIONS 87 4.5 FUTURE DIRECTIONS 90 4.6 CONCLUSION 91 REFERENCES 92 APPENDIX: DECLARATION OF HONOUR / EIGENSTÄNDIGKEITSERKLÄRUNG 131 / Background. Excessive worry is characterized by persistent, repetitive negative thoughts that are perceived as intrusive and uncontrollable. Chronic worrying can become a severely debilitating mental activity and is thought to contribute to the development, maintenance and deterioration of a range of somatic health problems and mental disorders. Theoretical accounts and empirical findings suggest that excessive worry is associated with impaired bottom-up salience-processing, insufficient top-down attentional control, deficits in emotion regulation and abnormal self-referential mental functions. Neuroimaging studies of excessive worry indicate functional activation and connectivity alterations in limbic and paralimbic brain structures that support reactivity to emotional stimuli, in prefrontal structures implicated in top-down processes underlying attentional control and emotion regulation, and in cortical midline structures involved in self-referential mental activity. However, with regard to the presence, the exact localization of the brain areas involved and the directionality of the effects, these studies have presented largely heterogenous results. The high variability of findings makes it difficult to achieve a coherent understanding of the neurobiological mechanisms of excessive worry. To extend this understanding and provide future directions for continued research in this area, the aim of this thesis was threefold: (i) to synthesize the emotional task-based fMRI literature on excessive worry in a quantitative, data-driven manner for the purpose of identifying consistent functional perturbations across studies; (ii) to determine the psychological processes with which the identified brain regions are associated and the functional brain networks in which they operate; and (iii) to examine abnormalities in basic brain organization associated with excessive worry. Methods. A state-of-the-art coordinate-based meta-analysis was conducted applying the activation likelihood estimation (ALE) algorithm to determine concordance among 16 neuroimaging experiments reporting alterations in brain functional activity during emotional processing between individuals experiencing high versus normal levels of worry. The identified regions were behaviorally characterized using functional magnetic resonance imaging (fMRI) metadata. Additionally, meta-analytic-connectivity modeling (MACM) was used to determine their global functional connectivity (FC) patterns and thus identify related brain networks. Finally, resting-state fMRI was used to compare FC patterns between 21 high and 21 low worriers in the absence of task-related brain activation. Dispositional worry was assessed using the Penn State Worry Questionnaire as a reliable self-report measure of severe worry. Seed-based analyses with the meta-analytically derived brain regions as seeds and a data-driven multi-voxel pattern analysis (MVPA) were performed to detect FC differences between the two groups. In addition, cross-group correlations between state worry levels and the FC patterns of the seed regions as well as the MVPA-derived component scores were analyzed. Results. The meta-analysis revealed convergent aberrations in high compared to normal worriers mainly in a left-hemispheric cluster comprising parts of the middle frontal gyrus, inferior frontal gyrus and anterior insula. Behavioral characterization indicated the identified cluster to be associated with language processing and memory. Furthermore, meta-analytic connectivity mapping yielded strong functional connections between the observed convergent regions and frontal, temporal, and parietal brain regions that overlap with parts of two behaviorally relevant brain networks, specifically the salience network (SN) and the default network (DN). The resting-state FC (rsFC) analyses revealed no differences between high and normal worriers and also no correlations between rsFC patterns and state worry, neither using the seed-based nor the MVPA approach. Conclusions. The results of this thesis indicate that excessive worry is related to disturbed functioning in brain areas that have been related to bottom-up and top-down attentional control as well as emotion generation and regulation. Behavioral analysis uncovered associations between the identified cluster and language processing that might be related to the exaggerated inner speech processes in worry prone individuals. This association has so far remained rather unnoticed and requires further exploration. Moreover, the identified brain regions constitute key nodes within interacting neural networks that support internally and externally oriented cognition and control the dynamic interplay among these processes. Their altered cross-network dynamics may underlie the inability of worry-prone individuals to disengage from internally oriented cognitions when adaptive responding would require an external focus of attention. The null-findings of the resting-state analyses might be due to the study design or caused by characteristics of worry itself, but are not interpreted as evidence that abnormalities in the brain's intrinsic connectivity associated with excessive worrying are absent. The results of this thesis may guide future research that could, for example, investigate whether and how the dynamic temporal interactions within and between the networks identified here differ depending on the severity of worry. The ALE results provide an a priori selection of brain regions for such studies. Increasing our understanding of the aberrations in brain networks that underlie excessive worry and the psychological functions that are impaired as a result will provide targets for improving therapeutic interventions.:Contents TABLES VIII FIGURES IX ABBREVIATIONS X ABSTRACT 1 1 THEORETICAL BACKGROUND 6 1.1 WORRY 6 1.1.1 DEFINITION, NATURE AND FUNCTION OF WORRY 6 1.1.2 THE WORRY CONTINUUM – NORMAL VERSUS MALADAPTIVE WORRY 7 1.1.3 THE DELETERIOUS EFFECTS OF EXCESSIVE WORRY 8 1.1.4 THEORETICAL MODELS OF EXCESSIVE WORRY 11 1.2 FUNCTIONAL BRAIN NETWORKS AND EXCESSIVE WORRY 18 1.2.1 A SYSTEMS NEUROSCIENCE VIEW OF EXCESSIVE WORRY 18 1.2.2 EMPIRICAL EVIDENCE: FMRI STUDIES ON EXCESSIVE WORRY 20 1.3 RESEARCH QUESTION 32 2 STUDY I: A QUANTITATIVE META-ANALYSIS OF FMRI STUDIES INVESTIGATING EMOTIONAL PROCESSING IN EXCESSIVE WORRIERS: APPLICATION OF ACTIVATION LIKELIHOOD ESTIMATION ANALYSIS 35 2.1 ABSTRACT 36 2.2 INTRODUCTION 37 2.3 METHODS 40 2.3.1 LITERATURE SEARCH AND STUDY SELECTION 40 2.3.2 ACTIVATION LIKELIHOOD ESTIMATION 46 2.3.3 META-ANALYTIC CONNECTIVITY MODELING 47 2.3.4 ANALYSIS OF BEHAVIORAL DOMAIN PROFILES 47 2.4 RESULTS 48 2.4.1 SIGNIFICANT ALE CLUSTERS 48 2.4.2 FUNCTIONAL CONNECTIVITY OF THE DERIVED ALE-CLUSTER – MACM-ANALYSIS 51 2.4.3 FUNCTIONAL CHARACTERIZATION OF THE DERIVED ALE-CLUSTER – BEHAVIORAL ANALYSIS 54 2.5 DISCUSSION 55 2.6 CONCLUSION 59 2.7 SUPPLEMENTARY MATERIAL STUDY I: LISTING OF ALE CLUSTERS SIGNIFICANT AT P < 0.001 UNCORRECTED, CLUSTER SIZE > 100MM3 60 3 STUDY II: HIGH AND LOW WORRIERS DO NOT DIFFER IN UNSTIMULATED RESTING-STATE BRAIN CONNECTIVITY 61 3.1 ABSTRACT 62 3.2 INTRODUCTION 63 3.3 MATERIALS AND METHODS 65 3.3.1 PARTICIPANTS AND PROCEDURE 65 3.3.2 FMRI DATA ACQUISITION 66 3.3.3 SELF-REPORT ASSESSMENTS AND STATE WORRY ASSESSMENT 66 3.3.4 STATISTICAL ANALYSES 67 3.4 RESULTS 69 3.4.1 SELF-REPORT MEASURES 69 3.4.2 FMRI RESULTS 72 3.5 DISCUSSION 72 3.6 CONCLUSION 75 3.7 SUPPLEMENTARY MATERIAL STUDY II: STATE WORRY ASSESSMENT 75 4 GENERAL DISCUSSION 76 4.1 CONVERGENT ABERRANT FUNCTION IN THE MFG-IFG-INSULA-CLUSTER 76 4.2 META-ANALYTIC FUNCTIONAL CHARACTERIZATION AND CONNECTIVITY MAPPING OF THE MFG-IFG-INSULA CLUSTER 82 4.3 NO RESTING-STATE FUNCTIONAL CONNECTIVITY DIFFERENCES BETWEEN HW AND LW 84 4.4 STRENGTHS AND LIMITATIONS 87 4.5 FUTURE DIRECTIONS 90 4.6 CONCLUSION 91 REFERENCES 92 APPENDIX: DECLARATION OF HONOUR / EIGENSTÄNDIGKEITSERKLÄRUNG 131

Doctor of Philosophy / Department of Statistics / Paul Nelson / Panels of judges are often used to estimate consumer preferences for m items such as food products. Judges can either evaluate each item on several ordinal scales and indirectly produce an overall ranking, or directly report a ranking of the items. A complete ranking orders all the items from best to worst. A partial ranking, as we use the term, only reports rankings of the best q out of m items. Direct ranking, the subject of this report, does not require the widespread but questionable practice of treating ordinal measurement as though they were on ratio or interval scales. Here, we develop and study segmentation models in which the panel may consist of relatively homogeneous subgroups, the segments. Judges within a subgroup will tend to agree among themselves and differ from judges in the other subgroups. We develop and study the statistical analysis of mixture models where it is not known to which segment a judge belongs or in some cases how many segments there are. Viewing segment membership indicator variables as latent data, an E-M algorithm was used to find the maximum likelihood estimators of the parameters specifying a mixture of Mallow’s (1957) distance models for complete and partial rankings. A simulation study was conducted to evaluate the behavior of the E-M algorithm in terms of such issues as the fraction of data sets for which the algorithm fails to converge and the sensitivity of initial values to the convergence rate and the performance of the maximum likelihood estimators in terms of bias and mean square error, where applicable. A Bayesian approach was developed and credible set estimators was constructed. Simulation was used to evaluate the performance of these credible sets as confidence sets. A method for predicting segment membership from covariates measured on a judge was derived using a logistic model applied to a mixture of Mallows probability distance models. The effects of covariates on segment membership were assessed. Likelihood sets for parameters specifying mixtures of Mallows distance models were constructed and explored.

The estimation of the frequency and phase of a complex exponential in additive white Gaussian noise (AWGN) is a fundamental and well-studied problem in signal processing and communications. A variety of approaches to this problem, distinguished primarily by estimation accuracy, computational complexity, and processing latency, have been developed. One class of approaches is based on the Fast Fourier Transform (FFT) due to its connections with the maximum likelihood estimator (MLE) of frequency. This thesis compares several FFT-based approaches to the MLE in terms of their estimation accuracy and computational complexity. While FFT-based frequency estimation tends to be very accurate, the computational complexity of the FFT and the latency associated with performing these computations after the entire signal has been received can be prohibitive in some scenarios. Another class of approaches that addresses some of these shortcomings is based on linear regression of samples of the instantaneous phase of the observation. Linear- regression-based techniques have been shown to be very accurate at moderate to high signal to noise ratios and have the additional benefit of low computational complexity and low latency due to the fact that the processing can be performed as the samples arrive. These techniques, however, typically require the computation of four-quadrant arctangents, which must be approximated to retain low computational complexity. This thesis proposes a new frequency and phase estimator based on simple estimates of the zero-crossing times of the observation. An advantage of this approach is that it does not require arctangent calculations. Simulation results show that the zero-crossing frequency and phase estimator can provide high estimation accuracy, low computational complexity, and low processing latency, making it suitable for real-time applications. Accordingly, this thesis also presents a real-time implementation of the zero-crossing frequency and phase estimator in the context of a time-slotted round-trip carrier synchronization system for distributed beamforming. The experimental results show this approach can outperform a Phase Locked Loop (PLL) implementation of the same distributed beamforming system.

Despite their success and widespread usage in industry and business, ES methods have received little attention from the statistical community. We investigate three types of statistical models that have been found to underpin ES methods. They are ARIMA models, state space models with multiple sources of error (MSOE), and state space models with a single source of error (SSOE). We establish the relationship among the three classes of models and conclude that the class of SSOE state space models is broader than the other two and provides a formal statistical foundation for ES methods. To better understand ES methods, we investigate the behaviors of ES methods for time series generated from different processes. We mainly focus on time series of ARIMA type. ES methods forecast a time series using only the series own history. To include covariates into ES methods for better forecasting a time series, we propose a new forecasting method, Exponential Smoothing with Covariates (ESCov). ESCov uses an ES method to model what left unexplained in a time series by covariates. We establish the optimality of ESCov, identify SSOE state space models underlying ESCov, and derive analytically the variances of forecasts by ESCov. Empirical studies show that ESCov outperforms ES methods and regression with ARIMA errors. We suggest a model selection procedure for choosing appropriate covariates and ES methods in practice. Computer models have been commonly used to investigate complex systems for which physical experiments are highly expensive or very time-consuming. Before using a computer model, we need to address an important question ``How well does the computer model represent the real system?" The process of addressing this question is called computer model validation that generally involves the comparison of computer outputs and physical observations. In this thesis, we propose a Bayesian approach to computer model validation. This approach integrates together computer outputs and physical observation to give a better prediction of the real system output. This prediction is then used to validate the computer model. We investigate the impacts of several factors on the performance of the proposed approach and propose a generalization to the proposed approach.

In this paper I derive the asymptotics of the exact, Euler, and Milstein ML estimators for diffusion models, including general nonstationary diffusions. Though there have been many estimators for the diffusion model, their asymptotic properties were generally unknown. This is especially true for the nonstationary processes, even though they are usually far from the standard ones. Using a new asymptotics with respect to both the time span T and the sampling interval ¢, I find the asymptotics of the estimators and also derive the conditions for the consistency. With this new asymptotic result, I could show that this result can explain the properties of the estimators more correctly than the existing asymptotics with respect only to the sample size n. I also show that there are many possibilities to get a better estimator utilizing this asymptotic result with a couple of examples, and in the second part of the paper, I derive the higher order asymptotics which can be used in the bootstrap analysis.

In this thesis, we expand the option pricing and virtual asset model system by Cheng (2005) and include new simulations and maximum likelihood estimation of the parameter of the stochastic differential equations. For easy manipulation of general users, the interface of original option pricing system is modified. In addition, in order to let the system more completely, some stochastic models and methods of pricing and estimation are added. This system can be divided into three major parts. One is an option pricing system; The second is an asset model simulation system; The last is estimation system of the parameter of the model. Finally, the analysis for the data of network are carried out. The differences of the prices between estimator of this system and real market are compared.