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Simultaneous testing of multiple null hypotheses has now become an integral part of statistical analysis of data arising from modern scientific investigations. Often the test statistics in such multiple testing problem are correlated. The research in this dissertation is motivated by the scope of improving or extending existing methods to incorporate correlation in the data. Sarkar (2008) proposes controlling the pairwise false discovery rate (Pairwise-FDR), which inherently takes into account the dependence among the p-values, thereby making it a more robust, less conservative and more powerful under dependence than the usual notion of FDR. In this dissertation, we further investigate the performance of Pairwise-FDR under a dependent mixture model. In particular, we consider a step-up method to control the Pairwise-FDR under this model assuming that the correlation between any two p-values is the same (exchangeable). We also suggest improving this method by incorporating an estimate of the number of pairs of true null hypotheses developed under this model. Efron (2007, Journal of the American Statistical Association 102, 93-103) proposed a novel approach to incorporate dependence among the null p-values into a multiple testing method controlling false discoveries. In this dissertation, we try to investigate the scope of utilizing this approach by proposing alternative versions of adaptive Bonferroni and BH methods which estimates the number of true null hypotheses from the empirical null distribution introduced by Efron. These newer adaptive procedures have been numerically shown to perform better than existing adaptive Bonferroni or BH methods within a wider range of dependence. A gene expression microarray data set has been used to highlight the difference in results obtained upon applying the proposed and other adaptive BH methods. Another approach to address the presence of correlation is motivated by the scope of utilizing the dependence structure of the data towards further improving some multiple testing methods while maintaining control of some error rate. The dependence structure of the data is incorporated using pairwise weights. In this dissertation we propose a weighted version of the pairwise FDR (Sarkar, 2008) using pairwise weights and a method controlling the weighted pairwise- FDR. We give a discussion on the application of such weighted procedure and suggest some weighting schemes that generates pairwise weights. / Statistics

As the availability of large datasets becomes more prevalent, so does the need to discover significant findings among a large collection of hypotheses. Multiple testing procedures (MTP) are used to control the familywise error rate (FWER) or the chance to commit at least one type I error when performing multiple hypotheses testing. When controlling the FWER, the power of a MTP to detect significant differences decreases as the number of hypotheses increases. It would be ideal to discover the same false null hypotheses despite the family of hypotheses chosen to be tested. Holland and Cheung (2002) developed measures called familywise robustness criteria (FWR) to study the effect of family size on the acceptance and rejection of a hypothesis. Their analysis focused on procedures that controlled FWER and false discovery rate (FDR). Newer MTPs have since been developed which control the generalized FWER (gFWER (k) or k-FWER) and false discovery proportion (FDP) or tail probabilities for the proportion of false positives (TPPFP). This dissertation reviews these newer procedures and then discusses the effect of family size using the FWRs of Holland and Cheung. In the case where the test statistics are independent and the null hypotheses are all true, the Type R enlargement familywise robustness measure can be expressed as a ratio of the expected number of Type I errors. In simulations, positive dependence among the test statistics was introduced, the expected number of Type I errors and the Type R enlargement FWR increased for step-up procedures with higher levels of correlation, but not for step-down or single-step procedures. / Statistics

The laboratory curriculum and assessment of the course Biology 2D03, The Plant Kingdom, was revised in 1998. In part, the revision was due to the need to update the laboratory manual to, reflect a new edition of the text book. Also revision to condense three chapters into two to accommodate a shorter than usual term and to include a chapter on the fungi was done. Assessment was revised in response to student suggestions and comments taken from course assessments. Key to these revisions was incorporating Multiple Intelligence theory into curriculum and assessment. A new form of assessment, mini-laboratory practicals, was devised replacing quizzes and one laboratory examination. The mini-laboratory practicals utilized visual-spatial, bodilykinesthetic, naturalist intelligence, verbal-linguistic and mathematical-logical intelligences. Intrapersonal intelligence was implemented with an essay assignment which required students to reflect on how plants were important to their personal lives. Musical-rhythmic intelligence was implemented by playing classical music with nature sounds (to enhance the naturalist intelligence) in the laboratory classroom. Two laboratory sections requested that the music be played during test situations while six sections did not. There were few unintended side effects of the revisions. The essay was more of a feminine exercise and male students had difficulty in relating personal experience. Revision of assessment procedures did not affect grade means or distributions. Assessment methods required some memorization but also required thinking and application of knowledge. A large proportion of students found that the combination of assessment methods (mini-laboratory practicals, laboratory examination and final examination) best tested their knowledge. The majority suggested that the new revision scheme be retained. The use of classical music with nature sounds resulted in a more relaxing, soothing learning environment but there was no evidence of a "Mozart effect". / Thesis / Master of Science (Teaching)

In a parallel distributed detection system each local detector makes a decision based on its own observations and transmits its local decision to a fusion center, where a global decision is made. Given fixed local decision rules, in order to design the optimal fusion rule, the fusion center needs to have perfect knowledge of the performance of the local detectors as well as the prior probabilities of the hypotheses. Such knowledge is not available in most practical cases. In this thesis, we propose a blind technique for the general distributed detection problem with multiple hypotheses. We start by formulating the optimal M-ary fusion rule in the sense of minimizing the overall error probability when the local decision rules are fixed. The optimality can only be achieved if the prior probabilities of hypotheses and parameters describing the local detector performance are known. Next, we propose a blind technique to estimate the parameters aforementioned as in most cases they are unknown. The occurrence numbers of possible decision combinations at all local detectors are multinomially distributed with occurrence probabilities being nonlinear functions of the prior probabilities of hypotheses and the parameters describing the performance of local detectors. We derive nonlinear Least Squares (LS) and Maximum Likelihood (ML) estimates of unknown parameters respectively. The ML estimator accounts for the known parametric form of the likelihood function of the local decision combinations, hence has a better estimation accuracy. Finally, we present the closed-form expression of the overall detection performance for both binary and M-ary distributed detection and show that the overall detection performance using estimated values of unknown parameters approaches quickly to that using their true values. We also investigate various impacts to the overall detection. The simulation results show that the blind algorithm proposed in this thesis provides an efficient way to solve distributed detection problems. / Thesis / Master of Applied Science (MASc)

An analysis is presented of the linear and geometrically nonlinear static response of "thin" doubly-curved shells of revolution, under internal pressure loading. The analysis is based upon direct numerical integration of the governing differential equations, written in first-order state vector form. It is assumed that the loading and response of the shell are both axially symmetric; the governing equations are thus ordinary differential equations. The geometry of the shell is limited in the analysis by the assumptions of axisymmetry and constant thickness. The shell is allowed to have general composite laminate construction, elastic supports at the edges and internal ring stiffeners. In addition, the analysis allows for the possibility of circumferential line loads at discrete locations along the dome meridian. The problem is a numerically unstable two-point boundary value problem; integrations are performed using the technique of multiple shooting. A development of the multiple shooting technique known as stabilized marching is given. Results achieved by use of the multiple shooting technique are verified by comparison to results of finite element analysis using the finite element analysis codes STAGS and ABAQUS. Parametric studies are performed for ellipsoidal domes constructed of symmetric, 8-ply laminates. The parametric studies examine the effects of dome geometry for a quasi-isotropic laminate first, then examine whether material properties may be adjusted to create a "better" design. Conclusions and recommendations for future work follow. / Ph. D.