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Mathematical models are often used to forecast interesting scientific phenomena. These models may provide a good approximation for the system being studied, but they are rarely perfect. Whether due to scientific misunderstandings or the necessity of numerically approximating the solution to the model, the mathematical models fail to exactly replicate the true dynamics of the system. This "model error" leads to forecast errors and degradation of forecast skill. The primary goal of this dissertation is to develop methods to correct a mathematical model with observed data, improving the accuracy of forecasts generated by the model. Correcting for model error is particularly difficult when the system is high-dimensional and when the state transition model is nonlinear. The methods developed in this dissertation are robust to both of these difficulties.The problem of estimating model error may be phrased as a parameter estimation problem within a filtering context. Many parameter estimation methods have been developed for the particle filter (PF), a filter with strong theoretical underpinnings and well understood large sample properties. Unfortunately, the PF fails when the state dimension is large. Instead, scientists who filter high-dimensional state-spaces typically use the ensemble Kalman filter (EnKF). This algorithm is effective in practice, but its large sample properties remain to be proven and methods for parameter estimation exist only in special cases. We make a newfound connection between these two algorithms: the EnKF is a regularized PF with additional approximations that have yet to be fully justified from a theoretical standpoint. Building on this connection, we introduce a novel algorithm that combines the best features of the EnKF and the PF. The EnKF is used to filter the high-dimensional state while an auxiliary PF is used to estimate the low-dimensional parameters; we call this filter the EnKF-APF. Using the Lorenz 2005 system, we demonstrate that th

Many problems in statistics are inherently discrete. When one of these problems also contains an optimization component, integer programming may be used to facilitate a solution to the statistical problem. We use integer programming techniques to help solve problems in the following areas: optimal blocking of a randomized controlled experiment with several treatment categories and statistical auditing using stratified random samples.We develop a new method for blocking in randomized experiments that works for an arbitrary number of treatments. We analyze the following problem: given a threshold for the minimum number of units to be contained in a block, and given a distance measure between any two units in the finite population, block the units so that the maximum distance between any two units within a block is minimized. This blocking criterion can minimize covariate imbalance, which is a common goal in experimental design. Finding an optimal blocking is an NP-hard problem. However, using ideas from graph theory, we provide the first polynomial time approximately optimal blocking algorithm for when there are more than two treatment categories. In the case of just two such categories, our approach is more efficient than existing methods. We derive the variances of estimators for sample average treatment effects under the Neyman-Rubin potential outcomes model for arbitrary blocking assignments and an arbitrary number of treatments. In addition, statistical election audits can be used to collect evidence that the set of winners (the outcome) of an election according to the machine count is correct---that it agrees with the outcome that a full hand count of the audit trail would show. The strength of evidence is measured by the p<\italic>-value of the hypothesis that the machine outcome is wrong. Smaller p<\italic>-values are stronger evidence that the outcome is correct. Most states that have election audits of any kind require audit samples stratified by

Background Inadequate consumption of dairy products without appropriate dietary substitution may have deleterious health consequences. Social research reveals the factors that may impede compliance with dietary recommendations. This is particularly important given the recent introduction of functional dairy products. One of the challenges for public health professionals is to demonstrate the efficacy of nutrition education in improving attitudes toward nutrient rich foods. The aim of this study was to explore the salient beliefs of adult weight loss trial participants regarding both traditional and functional dairy products and to compare these with a control group not exposed to nutrition education Methods Six focus groups were conducted, three with weight loss trial completers (n=15) that had received nutrition education and three with individuals from the same region (n=14) to act as controls. Transcribed focus groups were coded using the Theory of Planned Behaviour theoretical framework. Results Non-trial participants perceived dairy foods as weight inducing and were sceptical of functional dairy products. A lack of time/ability to decipher dairy food labels was also discussed by these individuals. In contrast trial participants discussed several health benefits related to dairy foods, practised label reading and were confident in their ability to incorporate dairy foods into their diet. Normative beliefs expressed were similar for both groups indicating that these were more static and less amenable to change through nutrition education than control and behavioural beliefs. Conclusions Nutrition education provided as a result of weight loss trial participation influenced behavioural and control beliefs relating to dairy products. This study provides a proof of concept indication that nutrition education may improve attitudes towards dairy products and may thus be an important target for public health campaigns seeking to increase intake of this food group.

Background Dairy products have been perceived as having the potential to cause adverse effects in individuals with Crohn’s disease (CD) and are often avoided, potentially increasing the risk of osteoporosis and related morbidity associated with inadequate dietary calcium intake. Objective To evaluate the self-reported effects of dairy products on CD symptoms and to determine whether these effects differed between types of dairy products consumed and disease state or location. Design Secondary analysis of dietary survey and clinical data from participants in the Genes and Diet in Inflammatory Bowel Disease study based in Auckland, New Zealand. Subjects/setting One hundred and sixty-five men and women diagnosed with CD for which both dietary survey data and clinical information were available. Statistical analyses performed 2 analysis was conducted to assess whether significant differences in the proportions of responses relating to a worsening of CD symptoms from individual dairy products were evident between individuals with active or quiescent CD, or ileal or colonic disease locations. Odds ratios with confidence interval were calculated to determine whether CD location was associated with risk of any type of adverse reaction to milk products. Logit scales were utilized to depict selfreported CD symptoms associated with individual dairy product consumption for ileal and colonic CD patients. Results Dairy products had no effect on self-reported CD symptoms for most people. Dairy products with a high fat content were most frequently reported to worsen perceived CD symptoms. Clinically, self-reported CD activity status did not influence responses to dairy products; however, colonic inflammation was more frequently associated with adverse CD effects in comparison to ileal CD involvement. Conclusions Research outcomes question the necessity of dairy product avoidance in CD patients and illustrate the highly individual nature of dairy product tolerance in this clinical p

Background Mycobacterium avium subspecies paratuberculosis (MAP) is an infective agent found in ruminants and milk products, which has been suggested to increase the risk of gastrointestinal inflammation in genetically susceptible hosts. It is hypothesized that lactase persistence facilitates exposure to such milk products increasing the likelihood of adverse outcomes. Individuals either homozygous or heterozygous for the T allele of DNA variant, rs4988235, located 14kb upstream from the LCT locus, are associated with having lactase persistence. The aim of this study was to determine whether lactase persistence as evident by the T allele of rs4988235 is associated with Crohn’s Disease (CD) in a New Zealand population. Findings Individuals homozygous for the T allele (T/T genotype) showed a significantly increased risk of having CD as compared with those homozygous for the C allele (OR=1.61, 95% CI=1.03-2.51). Additionally, a significant increase in the frequency of the T allele was observed in CD patients (OR=1.30, 95% CI=1.05-1.61, p=0.013), indicating that the T allele encoding lactase persistence was associated with an increased risk of CD. Conclusions Our findings indicate that lactase persistence as evident by the presence of the T allele of rs4988235 is associated with risk of CD in this New Zealand Caucasian population.

We have developed a model for teaching math- ematical statistics through detailed case studies, and we have had some success with students us- ing the R and S-Plus languages to analyze data from the cases and to perform simulation studies of statistical concepts underlying the methods used in the analyses. We describe a few examples of these simulation studies, and explain how we use the computer to bridge the gap between statistical theory and practice and to develop understanding of the the basic ideas in mathematical statistics. Recently, we have embarked on a new approach that builds on the work of the Omegahat project (www.omegahat.org), which has embedded the R statistical software in the Netscape browser. We are designing interactive environments for browsers that use R for performing computations and plot- ting. The goal is to develop electronic activities that will make it easier for students to explore and develop understanding of the concepts of statistics and that will connect these concepts to the practice of statistics.

The spectacular growth and acceptance of theWeb has made it a very attractive medium for interactive documents. Web-based reporting in industry, “live” documents in research, and interactive worksheets in education material are in many ways ideal uses of the Web. These types of documents frequently display dynamic, statistical output both in the form of text and plots. Unfortunately, much of the effort in creating these types of documents has focussed on re-inventing existing statistical software, and often with inferior results. The reason is that systems such as S and SAS cannot be integrated into the reader’s browser. A better approach is to allow the author to create a document using the common authoring tools (e.g. LATEX, MS Word or HTML editors) and to conveniently insert dynamic and interactive components from other languages. The author focuses on the presentation and display of these components, including the usual multi-media elements such as text, images and sounds. She uses HTML form elements and Java components to provide interactive controls with which the reader can manipulate the contents of the document. And finally she performs statistical computations and renders visual displays using the statistical software that is embedded within the reader’s browser. In this presentation, we describe how we have created an environment for interactive statistical documents. It allows the author to use HTML, JavaScript and R to create the content and the interactivity. The reader accesses the interactive and dynamic functionality of the document via a plug-in for Netscape that embeds R within it. The different languages are all reasonably standard tools and each is used for the purposes for which it was designed. This makes it a reasonably straightforward environment in which to quickly and simply create interfaces for various different applications and audiences.