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David A. Castanon, Bernard C. Levy, Alan S. Willsky. / "May 1979." / Bibliography: leaf 29-31. / Office of Naval Research contract ONR/N00014-76-C-0346

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This work deals with statistical tests of association between genetic markers and disease phenotypes. The main criterion used for comparing the tests is statistical power. First we consider animal models and then data from association studies of humans. For the animal section, we analyse a dataset from a prominent mouse experiment which developed a heterogeneous stock of mice via multiple crosses. This stock is characterised by small distances between recombinants which allows fine mapping of genetic loci, but also by uncertainty in haplotypes. We start by highlighting the disadvantages of the currently used approach to deal with this uncertainty and suggest a method that has greater statistical power and is computationally efficient. The method applies the EM algorithm to the broad class of exponential family distributions of phenotypes. We also develop a Bayesian version of the method, for which we extend the widely used IRLS algorithm to maximisation of the weighted posterior. Then we move on to genome-wide association studies (GWAS), where two situations are considered: known and unknown minor allele frequency. First we develop an innovative Bayesian model with the optimal prior for the known population MAF. We demonstrate that not only it is more powerful than any frequentist test considered (the size of the advantage depends on prevalence of the disease and MAF), but also that the frequentist tests change ranking in terms of power. A remarkable property of the frequentist tests, the advantage of discarding part of the data to gain power, is highlighted. The second chapter on GWAS considers the currently more common situation of the unknown MAF, when the Armitage test is known to be the most powerful frequentist method. We show that the suggested model is more powerful in the broad selection of settings considered, including the three different allele effect models: additive, dominant and recessive. For both known and unknown MAF cases we point out that the parameters are constrained and demonstrate how to gain power by taking this constraint into account.

Thesis (MTech (Cartography))--Cape Peninsula University of Technology, 2016. / This case study investigates the change in the geographical boundaries by creating a Spatio-temporal mapping of Ciskei (one of the so-called Bantustans or Homelands) during the period of Apartheid. It examines the reasons for its establishment, and what impact the apartheid land legislation had on the geographical boundaries of Ciskei. GIS technology was used in this study to create time series animation and Static map to display the spatial change of the Ciskei boundaries. This investigation was split into quantitative and qualitative assessments. The aim of the quantitative assessments was to determine the amount of the spatial change of the Ciskei geographic boundary. The qualitative methods was used to investigate the map viewer’s understanding of the amount of the information in the static and animated maps. The results of qualitative assessments showed that static and animated maps have their respective advantages in the visualization of the map viewer. The importance of this research is to take advantage of time series mapping techniques to study the homeland areas in South Africa and see all the changes that have occurred as a result of a period of apartheid legislation. For this research, the following data were gathered: Attribute and metadata was the legislation and laws related to the land and the geographic data was the historical maps and coordinate data.

In this thesis, we investigate the estimation problem and inference problem for the complex models. Two major categories of complex models are emphasized by us, one is generalized linear models, the other is time series models. For the generalized linear models, we consider one fundamental problem about sure screening for interaction terms in ultra-high dimensional feature space; for time series models, an important model assumption about Markov property is considered by us. The first part of this thesis illustrates the significant interaction pursuit problem for ultra-high dimensional models with two-way interaction effects. We propose a simple sure screening procedure (SSI) to detect significant interactions between the explanatory variables and the response variable in the high or ultra-high dimensional generalized linear regression models. Sure screening method is a simple, but powerful tool for the first step of feature selection or variable selection for ultra-high dimensional data. We investigate the sure screening properties of the proposal method from theoretical insight. Furthermore, we indicate that our proposed method can control the false discovery rate at a reasonable size, so the regularized variable selection methods can be easily applied to get more accurate feature selection in the following model selection procedures. Moreover, from the viewpoint of computational efficiency, we suggest a much more efficient algorithm-discretized SSI (DSSI) to realize our proposed sure screening method in practice. And we also investigate the properties of these two algorithms SSI and DSSI in simulation studies and apply them to some real data analyses for illustration. For the second part, our concern is the testing of the Markov property in time series processes. Markovian assumption plays an extremely important role in time series analysis and is also a fundamental assumption in economic and financial models. However, few existing research mainly focused on how to test the Markov properties for the time series processes. Therefore, for the Markovian assumption, we propose a new test procedure to check if the time series with beta-mixing possesses the Markov property. Our test is based on the Conditional Distance Covariance (CDCov). We investigate the theoretical properties of the proposed method. The asymptotic distribution of the proposed test statistic under the null hypothesis is obtained, and the power of the test procedure under local alternative hypothesizes have been studied. Simulation studies are conducted to demonstrate the finite sample performance of our test.

Abstract Seasonal variations of events are apparently playing an important part in various psychiatric conditions. To study the seasonal variation of a condition appears to be one useful approach to clarify the aetiology of a mental disorder and phenomena to which mental disorders are associated. In the present study the seasonal variations of suicides during the period of 1980-95 (n=21279) and homicides during the years 1957-95 (n=4553) in Finland were analysed. In addition, the use of statistical techniques for seasonality and some important characteristics of study samples were evaluated from 44 original suicide seasonality studies published between 1970-97. Special attention was paid to statistical methods for seasonality and these were reviewed in the summary part of this dissertation. A statistically significant spring peak of suicides was found in both genders, in all age groups (aged 39 years or below, 40-64 years, and 65 years or more) and in violent (hanging, drowning, shooting, wrist-cutting, jumping from a height) and non-violent suicides (poisoning, gas, other methods). A secondary autumn peak of suicides was present in females and also associated with non-violent methods. The rate of violent suicides had increased significantly during 1980-90 and decreased thereafter, while the non-violent suicides had kept steadily increasing over the whole 16-year study period. The seasonal variation of violent suicides had remained stable and statistically significant over the whole study period, but the seasonality in non-violent suicides has diminished over time. The seasonal pattern of homicides showed a statistically significant peak in summer and a trough in winter. The observed rate of homicides was about 6% higher in summer and 6% lower in winter than expected under the null hypothesis of a uniform distribution. Both the crude numbers of homicide and the rate of homicides per 100 000 population increased significantly over the 39-year study period. The increasing rate of homicides in Finland was accompanied by decreasing homicide seasonality. The seasonal trends in homicides correlated significantly (positive correlation) with the seasonal trends in the violent suicides over the period of 1980-95. The use of particular statistical techniques was specified in the majority of the 44 reviewed suicide seasonality articles. This was considered as satisfactory, although in subgroup analyses and in comparisons of the seasonal pattern of suicides with phenomena other than suicides, researchers tended to interpret their study findings without a statistical significance test. In those 37 articles, which had actually examined the seasonal pattern of suicides with a statistical test, statistical methods varied from simple standard tests like the chi-square test (14 articles, 38%) to sophisticated time series analyses such as a spectral analysis (4 articles, 11%). The calendar effect (i.e. effect due to the unequal lengths of months and leap years) was reported to have been taken into account in only 10 out of 44 (22%) reviewed studies. The lack of reporting the size of a sample (12 articles, 27%) or monthly values of suicides (17 articles, 54%) was found to be a major deficit in the reviewed studies. On the basis of these findings it is recommended to carry out further surveys, which evaluate statistical content and use of statistical methods in published medical articles. These kinds of surveys remind researchers to consider more thoroughly methodological and statistical issues in their investigations.

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