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In evolutionary biology, genetic sequences carry with them a trace of the underlying tree that describes their evolution from a common ancestral sequence. Inferring this underlying tree is challenging. We investigate some curious cases in which different methods like Maximum Parsimony, Maximum Likelihood and distance-based methods lead to different trees. Moreover, we state that in some cases, ancestral sequences can be more reliably reconstructed when some of the leaves of the tree are ignored - even if these leaves are close to the root. While all these findings show problems inherent to either the assumed model or the applied method, sometimes an inaccurate tree reconstruction is simply due to insufficient data. This is particularly problematic when a rapid divergence event occurred in the distant past. We analyze an idealized form of this problem and determine a tight lower bound on the growth rate for the sequence length required to resolve the tree (independent of any particular branch length). Finally, we investigate the problem of intermediates in the fossil record. The extent of ‘gaps’ (missing transitional stages) has been used to argue against gradual evolution from a common ancestor. We take an analytical approach and demonstrate why, under certain sampling conditions, we may not expect intermediates to be found.

Ecological problems often require multivariate analyses. Ever since Bray and Curtis (1957) drew an analogy between Euclidean distance and community dissimilarity, most multivariate ecological inference has been based on geometric ideas. For example, ecologists routinely use distance-based ordination methods (e.g. multidimensional scaling) to enhance the interpretability of multivariate data. More recently, distance-based diversity indices that account for functional differences between species are now routinely used. But in most other areas of science, inference is based on Fisher's (1922) likelihood concept; statisticians view likelihood as an advance over purely geometric approaches. Nevertheless, likelihood-based reasoning is rare in multivariate statistical ecology. Using ordination and functional diversity as case studies, my thesis addresses the questions: Why is likelihood rare in multivariate statistical ecology? Can likelihood be of practical use in multivariate analyses of real ecological data? Should the likelihood concept replace multidimensional geometry as the foundation for multivariate statistical ecology? I trace the history of quantitative plant ecology to argue that the geometric focus of contemporary multivariate statistical ecology is a legacy of an early 20th century debate on the nature of plant communities. Using the Rao-Blackwell and Lehmann-Scheffé theorems, which both depend on the likelihood concept, I show how to reduce bias and sampling variability in estimators of functional diversity. I also show how to use likelihood-based information criteria to select among ordination methods. Using computationally intensive Markov-chain Monte Carlo methods, I demonstrate how to expand the range of likelihood-based ordination procedures that are computationally feasible. Finally, using philosophical ideas from formal measurement theory, I argue that a likelihood-based multivariate statistical ecology outperforms the geometry-based alternative by providing a stronger connection between analysis and the real world. Likelihood should be used more often in multivariate ecology.

Diese empirische Arbeit untersucht Determinanten des Renteneintritts. Sie basiert auf einem Optionswertmodell, um die Bedeutung finanzieller Überlegungen für ein Aufschieben des Renteneintritts zu analysieren. Zusätzlich wird der Einfluss institutioneller Rahmenbedingungen betrachtet. Ein neu verfügbarer Datensatz des Verbands Deutscher Rentenversicherungsträger wird dazu verwendet. Die Ergebnisse zeigen, dass Arbeitslosigkeit und Krankheit zu einem großen Teil einen frühen Renteneintritt erklären. Zusätzlich hat der Optionswert einen großen Erklärungsgehalt. / This paper empirically investigates determinants of retirement decisions. It is based on the option value approach to assess the importance of financial considerations for delaying immediate retirement. In addition, the impact of institutional conditions is considered. Newly available data from the data base of the statutory pension organization providing exact information about income, pension claims, and unemployment spells is used. The results indicate that unemployment and illness explain a great portion of early retirements. Additionally, the option value has explanatory power.

We consider the problem of maximum likelihood estimation of logistic sinusoidal regression models and develop some asymptotic theory including the consistency and joint rates of convergence for the maximum likelihood estimators. The key techniques build upon a synthesis of the results of Walker and Song and Li for the widely studied sinusoidal regression model and on making a connection to a result of Radchenko. Monte Carlo simulations are also presented to demonstrate the finite-sample performance of the estimators

Philosophiae Doctor - PhD / Malaria is a common infection in tropical areas, transmitted between humans through female anopheles mosquito bites as it seeks blood meal to carry out egg production. The infection forms a direct threat to the lives of many people in South Sudan. Reports show that malaria caused a large proportion of morbidity and mortality in the fledgling nation, accounting for 20% to 40% morbidity and 20% to 25% mortality, with the majority of the affected people being children and pregnant mothers. In this thesis, we construct and analyze mathematical models for malaria transmission in South Sudan context incorporating national malaria control strategic plan. In addition, we investigate important factors such as climatic conditions and population mobility that may drive malaria in South Sudan. Furthermore, we study a stochastic version of the deterministic model by introducing a white noise.

All pharmaceutical products are required by law to display an expiry date on the packaging. The period between the date of manufacture and expiry date is known as the label shelf-life. The label shelf-life indicates the period of time during which the consumer can expect the product to be safe and effective. Methods for determining the label shelf-life from stability data are discussed in the guidelines on the evaluation of stability data issued by the International Conference for Harmonization. These methods are limited to data that can be analysed using linear model methods. Furthermore, in the situation where a number of batches are used to determine a label shelf-life, the current regulatory method (unintentionally) penalizes good statistical design. In addition, the label shelf-life obtained this way may not be a reliable guide to the properties of future batches produced under similar conditions. In this thesis it is shown that the current definition of the label shelf-life may not provide the consumer with the desired level of confidence that the product is safe and effective. This is especially the case when the manufacturer has performed a well designed stability study with many assays. Consequently, a new definition for the label shelf-life is proposed, such that the consumer can be confident that a certain percentage of the product will meet the specification by the expiry date. Several methods for obtaining such a label shelf-life under linear model and generalized linear model assumptions are proposed and evaluated using simulation studies. The new definition of label shelf-life is extended to allow a label shelf-life to be obtained from stability studies that make use of many batches, such that a proportion of product over all batches can be assured to meet specifications by the expiry date. Several methods for estimating the label shelf-life in the multi-batch case are proposed and evaluated with the help of simulation studies. / Thesis (Ph.D.)--School of Agriculture and Wine, 2003.

<p>Forskning visar att budskap uppfattas olika beroende på perifera egenskaper. Syftet var att undersöka om man uppfattar personer från olika yrkesgrupper olika kopplade till samma budskap. En enkät inleddes med ett citat från en tidningsartikel. Deltagarna (<em>N </em>= 84) bedömde personen bakom uttalandet i fråga om grad av främlingsfientlighet respektive omsorg; i hälften angavs att en åklagare uttalat sig, i andra hälften en familjepedagog. Resultatet visade att det fanns en tendens till huvudeffekt att åklagaren skattades som fientligare än familjepedagogen samt en tendens att de med annan etnicitet skattade budskapet mer fientligt än etniskt svenska. Studien stödjer delvis antagandet att yrkesgrupp har betydelse för hur budskap uppfattas.</p>

In statistics it is of interest to find a better interval estimator of the absolute mean deviation. In this thesis, we focus on using the jackknife, the adjusted and the extended jackknife empirical likelihood methods to construct confidence intervals for the mean absolute deviation of a random variable. The empirical log-likelihood ratio statistics is derived whose asymptotic distribution is a standard chi-square distribution. The results of simulation study show the comparison of the average length and coverage probability by using jackknife empirical likelihood methods and normal approximation method. The proposed adjusted and extended jackknife empirical likelihood methods perform better than other methods for symmetric and skewed distributions. We use real data sets to illustrate the proposed jackknife empirical likelihood methods.

Longitudinal data arise commonly in many fields including public health studies and survey sampling. Valid inference methods for longitudinal data are of great importance in scientific researches. In longitudinal studies, data collection are often designed to follow all the interested information on individuals at scheduled times. The analysis in longitudinal studies usually focuses on how the data change over time and how they are associated with certain risk factors or covariates. Various statistical models and methods have been developed over the past few decades. However, these methods could become invalid when data possess additional features. First of all, incompleteness of data presents considerable complications to standard modeling and inference methods. Although we hope each individual completes all of the scheduled measurements without any absence, missing observations occur commonly in longitudinal studies. It has been documented that biased results could arise if such a feature is not properly accounted for in the analysis. There has been a large body of methods in the literature on handling missingness arising either from response components or covariate variables, but relatively little attention has been directed to addressing missingness in both response and covariate variables simultaneously. Important reasons for the sparsity of the research on this topic may be attributed to substantially increased complexity of modeling and computational difficulties. In Chapter 2 and Chapter 3 of the thesis, I develop methods to handle incomplete longitudinal data using the pairwise likelihood formulation. The proposed methods can handle longitudinal data with missing observations in both response and covariate variables. A unified framework is invoked to accommodate various types of missing data patterns. The performance of the proposed methods is carefully assessed under a variety of circumstances. In particular, issues on efficiency and robustness are investigated. Longitudinal survey data from the National Population Health Study are analyzed with the proposed methods. The other difficulty in longitudinal data is model selection. Incorporating a large number of irrelevant covariates to the model may result in computation, interpretation and prediction difficulties, thus selecting parsimonious models are typically desirable. In particular, the penalized likelihood method is commonly employed for this purpose. However, when we apply the penalized likelihood approach in longitudinal studies, it may involve high dimensional integrals which are computationally expensive. We propose an alternative method using the composite likelihood formulation. Formulation of composite likelihood requires only a partial structure of the correlated data such as marginal or pairwise distributions. This strategy shows modeling tractability and computational cheapness in model selection. Therefore, in Chapter 4 of this thesis, I propose a composite likelihood approach with penalized function to handle the model selection issue. In practice, we often face the model selection problem not only from choosing proper covariates for regression predictor, but also from the component of random effects. Furthermore, the specification of random effects distribution could be crucial to maintain the validity of statistical inference. Thus, the discussion on selecting both covariates and random effects as well as misspecification of random effects are also included in Chapter 4. Chapter 5 of this thesis mainly addresses the joint features of missingness and model selection. I propose a specific composite likelihood method to handle this issue. A typical advantage of the approach is that the inference procedure does not involve explicit missing process assumptions and nuisance parameters estimation.