The main objective of our study is to employ copula methodology to develop Bayesian hierarchical models to study the dependencies exhibited by temporal, spatial and spatio-temporal processes. We develop hierarchical models for both discrete and continuous outcomes. In doing so we expect to address the dearth of copula based Bayesian hierarchical models to study hydro-meteorological events and other physical processes yielding discrete responses. First, we present Bayesian methods of analysis for longitudinal binary outcomes using Generalized Linear Mixed models (GLMM). We allow flexible marginal association among the repeated outcomes from different time-points. An unique property of this copula-based GLMM is that if the marginal link function is integrated over the distribution of the random effects, its form remains same as that of the conditional link function. This unique property enables us to retain the physical interpretation of the fixed effects under conditional and marginal model and yield proper posterior distribution. We illustrate the performance of the posited model using real life AIDS data and demonstrate its superiority over the traditional Gaussian random effects model. We develop a semiparametric extension of our GLMM and re-analyze the data from the AIDS study. Next, we propose a general class of models to handle non-Gaussian spatial data. The proposed model can deal with geostatistical data that can accommodate skewness, tail-heaviness, multimodality. We fix the distribution of the marginal processes and induce dependence via copulas. We illustrate the superior predictive performance of our approach in modeling precipitation data as compared to other kriging variants. Thereafter, we employ mixture kernels as the copula function to accommodate non-stationary data. We demonstrate the adequacy of this non-stationary model by analyzing permeability data. In both cases we perform extensive simulation studies to investigate the performances of the posited models under misspecification. Finally, we take up the important problem of modeling multivariate extreme values with copulas. We describe, in detail, how dependences can be induced in the block maxima approach and peak over threshold approach by an extreme value copula. We prove the ability of the posited model to handle both strong and weak extremal dependence and derive the conditions for posterior propriety. We analyze the extreme precipitation events in the continental United States for the past 98 years and come up with a suite of predictive maps.

In many data sets, a mixture distribution formulation applies when it is known that each observation comes from one of the underlying categories. Even if there are no apparent categories, an implicit categorical structure may justify a mixture distribution. This thesis concerns the modeling of extreme values in such a setting within the peaks-over-threshold (POT) approach. Specifically, the traditional POT modeling using the generalized Pareto distribution is augmented in the sense that, in addition to threshold exceedances, data below the threshold are also modeled by means of the mixture exponential distribution. In the first part of this thesis, the conventional frequentist approach is applied for data modeling. In view of the mixture nature of the problem, the EM algorithm is employed for parameter estimation, where closed-form expressions for the iterates are obtained. A simulation study is conducted to confirm the suitability of such method, and the observation of an increase in standard error due to the variability of the threshold is addressed. The model is applied to two real data sets, and it is demonstrated how computation time can be reduced through a multi-level modeling procedure. With the fitted density, it is possible to derive many useful quantities such as return periods and levels, value-at-risk, expected tail loss and bounds for ruin probabilities. A likelihood ratio test is then used to justify model choice against the simpler model where the thin-tailed distribution is homogeneous exponential. The second part of the thesis deals with a fully Bayesian approach to the same model. It starts with the application of the Bayesian idea to a special case of the model where a closed-form posterior density is computed for the threshold parameter, which serves as an introduction. This is extended to the threshold mixture model by the use of the Metropolis-Hastings algorithm to simulate samples from a posterior distribution known up to a normalizing constant. The concept of depth functions is proposed in multidimensional inference, where a natural ordering does not exist. Such methods are then applied to real data sets. Finally, the issue of model choice is considered through the use of posterior Bayes factor, a criterion that stems from the posterior density. / published_or_final_version / Statistics and Actuarial Science / Master / Master of Philosophy

In the years immediately following the 1990 reunification of Germany, an increase in anti-foreigner violence threatened the stability of reunification efforts and exacerbated tensions between the East and the West. This paper is concerned with analyzing the underlying causes of the increase in anti-foreigner violence in Germany in the 1990s by evaluating first the period of reunification and the corresponding rise in support for extreme right groups in the former-East Germany. In addition, the history of violence and anti-foreigner sentiment in both East and West Germany are analyzed in conjunction with tensions caused by reunification to ascertain the origins of the post-reunification rise in xenophobic violence. Through this analysis, I show that violence in Germany in the early-1990s cannot be connected to the National Socialist past but rather, that both increases in anti-foreigner sentiment and corresponding violence result from a history in East and West Germany of ethnocentrism and social-exclusion policies directed at foreigners. Finally, this paper focuses on evaluating whether the post-reunification rise of violence in Germany is a unique event or whether it can be better understood as a wider European phenomenon. / text

published_or_final_version / abstract / toc / Statistics and Actuarial Science / Doctoral / Doctor of Philosophy

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The problem of efficient estimation of the parameters of the extreme value distribution has not been addressed in the literature. We obtain efficient estimators of the parameters of type I (maximum) extreme value distribution without solving the likelihood equations. This research provides for the first time simple expressions for the elements of the information matrix for type II censoring. We construct efficient estimators of the parameters using linear combinations of order statistics of a random sample drawn from the population. We derive explicit formulas for the information matrix for this problem for type II censoring and construct efficient estimators of the parameters using linear combinations of available order statistics with additional weights to the smallest and largest order statistics. We consider numerical examples to illustrate the applications of the estimators. We also perform an extensive Monte Carlo simulation study to examine the performance of the estimators for different sample sizes.

This thesis analyses ideas of gender in the Swedish radical right. The aim of the study is to see if there are any differences or similarities in the way gender is being formulated by a populist radical right party as the Sweden Democrats (Sverigedemokraterna), the extreme right party, Party of the Swedes (Svenskarnas Parti) and the extreme right movement Swedish Resistance Movement (Svenska Motståndsrörelsen). Ideas of gender are presented in the theory chapter which is used later on in the analysis to compare with the radical right organisations of Sweden. To fulfil the aim we have performed a comparative ideological analysis between the three organisations and the base for our analysis is texts from each organisation’s webpage. The study shows that the ideological differences concerning gender between populism and extremism in the Swedish radical right are relatively small

This Thesis examines the ideology, politics and organization of the Australian Extreme Right 1975-1995. Its central interpretative theme is the response of the Extreme Right to the development of the Australian State from a conservative Imperial structure into an American "anti-communist" client state, and ultimately into a liberal-internationalist machine which integrated Australia into a globalized capitalist order. The Extreme Right after 1975 differed from the various paramilitaries of the 1930's and the conservative anti-communist auxiliary organizations of the 1945-75 period. Post 1975, it lost its preoccupation with fighting the Left, and progressively grew as a challenger to liberal-internationalism. The abandonment of "White Australia" and consequent non-European immigration were the formative catalysts of a more diverse and complex Extreme Right. The Thesis uses a working definition of generic fascism as "palingenetic populist ultra-nationalism", to measure the degree of ideological and political radicalization achieved by the Extreme Right. This family of political ideas, independent of the State and mobilized beyond the limits of the former-period auxiliary conservatives, expressed itself in an array of organizational forms. The complexity of the Extreme Right can be demonstrated by using four typologies: Radical Nationalism, Neo-Nazism, Populist-Monarchism and Radical-Populism, each with specific points to make about social clienteles, geographical distribution, particular ideological heritages, and varied strategies and tactics. The Extreme Right could mobilize from different points of opportunity if political space became available. Inevitably a mutual delegitimization process between State and Extreme Right led to public inquiries and the emplacement of agencies and legislation to restrict the new radicalism. This was understandable since some Extreme Right groups employed violence or appeared to perform actions preparatory thereto. It also led to show-trials and para-State crime targeted against particular groups especially in the period 1988-91. Thereafter, Extreme Right organizations pursued strategies which led to electoral breakthroughs, both rural and urban as a style of Right-wing populist politics unfolded in the 1990's. It was in this period that the Extreme Right encouraged the co-optation by the State of the residual Left in the anti-racist fight. This seemed natural, as the Extreme Right's vocal references to popular democracy, national independence and the nativist heritage, had permitted it to occupy the Old Left's traditional ground. In that way too, it was "The Other Radicalism".

Thesis--Auburn University, 2009. / Abstract. Vita. Includes bibliographical references (p. 73-75).