Browsing by Subject "Multivariate"

Now showing 1 - 3 of 3
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    Bayesian Hierarchical Models For Multi-Variant and Multi-Trait Genome-Wide Association Studies
    (2020-06) Yang, Yi
    While genome-wide association studies (GWASs) have been widely used to identify associations between complex diseases and genetic variants, standard single-variant and single-trait analyses often have limited power when applied to scenarios in which variants are in linkage disequilibrium, occur at low frequency, or are associated with multiple correlated traits. In this dissertation, we propose three Bayesian hierarchical models for multi-variant and multi-trait GWASs based on the hierarchically structured variable selection (HSVS) framework: the generalized fused HSVS (HSVS-GF), the adaptive HSVS (HSVS-A), and the multivariate HSVS (HSVS-M). HSVS is a discrete mixture prior composed of a point mass at zero and a multivariate scale-mixing normal distribution for modeling the effects of variants. As an extension and development of the HSVS framework, the proposed methods have the flexibility to account for various correlation structures, which allows them to extensively borrow strength from multiple correlated variants and traits. As Bayesian methods, they can also integrate complex genetic information into the priors and thus boost the power by leveraging information from various sources. In addition to testing associations, the proposed methods in the Bayesian framework also produce posterior effect estimates for individual variants simultaneously, a distinctive and useful feature that most of the competing methods do not possess. Specifically, HSVS-GF is a pathway-based method that uses summary statistics and pathway structural information to identify the association of a disease with variants in a pathway. HSVS-A is a set-based method that tests the association of a continuous or dichotomous trait with rare variants in a set and estimates the effects of individual rare variants. HSVS-M is a multi-variant and multi-trait method that uses summary statistics both to test the association of variants in a gene with multiple correlated traits and to estimate the strength of association of the gene with each trait. Through analysis of simulated data in various scenarios and GWAS data from the Wellcome Trust Case Control Consortium and the Global Lipids Genetics Consortium, we show that the proposed methods can substantially outperform the competing methods and identify novel causal variants.
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    Gaussian-Pareto Overbounding: A Method for Managing Risk in Safety-Critical Navigation Systems
    (2018-06) Larson, Jordan
    An innovative method for managing the integrity risk of safety-critical navigation systems is presented. The method builds upon the current statistical technique used in the field of navigation known as overbounding which uses conservative probability distributions to bound risk probabilities. In particular, this work replaces the Gaussian distribution currently in use with a hybrid Gaussian-Pareto distribution. This change is motivated by results from Extreme Value Theory (EVT) and a simulation study assessing the Pareto distribution's potential as a model for the tails of distributions. Both of which are discussed thoroughly. By utilizing the hybrid Gaussian-Pareto overbound, the extreme error probabilities for distributions that display heavier-than-Gaussian tails can be truly overbounded which is necessary for constructing system output overbounds from input overbounds. The model also uses observed data more efficiently than current methods because it separates the extreme portion of the distribution from the core portion. Furthermore, the model can be less conservative than the Gaussian distribution across the entire domain which would lead to greater availability. To demonstrate this, the Gaussian-Pareto overbound is shown to be an appropriate model for double-differenced pseudoranges from two Continuously Operating Reference Stations (CORS) of the Global Navigation Satellite System (GNSS), an important measurement in many safety-critical navigation systems. Lastly, a novel approach for overbounding multivariate probability risks called norm overbounding is developed so that the Gaussian-Pareto model can be applied in the multivariate domain. This approach utilizes hyperspherical coordinates as well as domain partitioning in order to construct a robust model for bounding norms of random vectors which can be considered as multivariate errors. It is demonstrated for a simple 2-dimensional navigation application.
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    A nonparametric change point model for multivariate phase-II statistical process control.
    (2011-05) Holland, Mark David
    Phase-II statistical process control (SPC) procedures are designed to detect a change in distribution when a possibly never-ending stream of observations is collected. Extensive study has been conducted with the purpose of detecting a shift in location (e.g. mean or median) when univariate observations are collected. Many techniques have also been proposed to detect a shift in location vector when each observation consists of multiple measurements. These procedures require the user to make assumptions about the distribution of the process readings, to assume that process parameters are known, or to collect a large training sample before monitoring the ongoing process for a change in distribution. We propose a nonparametric procedure for multivariate phase-II statistical process control that does not require the user to make strong assumptions, or to collect a large training sample before monitoring the process for a shift in location vector.