Contributions to modeling parasite dynamics and dimension reduction

Bayesian hierarchical model;Infection rate;Markov chain Monte Carlo;Panel data;Dimension reduction;Fisher discriminant analysis

Cui, Na

关键词: Bayesian hierarchical model;    Infection rate;    Markov chain Monte Carlo;    Panel data;    Dimension reduction;    Fisher discriminant analysis;   

Others  :  https://www.ideals.illinois.edu/bitstream/handle/2142/32062/Cui_Na.pdf?sequence=1&isAllowed=y

美国|英语

来源: The Illinois Digital Environment for Access to Learning and Scholarship

【 摘 要 】

For my thesis, I have worked on two projects: modeling parasite dynamics (Chapter 2) and complementary dimensionality analysis (Chapter 3).In the first project, we study a longitudinal data of infection with the parasite Giardia lamblia among children in Kenya. Understanding the infection and recovery rate from parasitic infections is valuable for public health planning. Two challenges in modeling these rates are (1) infection status is only observed at discrete times even though infection and recovery take place in continuous time and (2) detectability of infection is imperfect. We address these issues through a Bayesian hierarchical model based on a random effects Weibull distribution. The model incorporates heterogeneity of the infection and recovery rate among individuals and allows for imperfect detectability. We estimate the model by a Markov chain Monte Carlo algorithm with data augmentation. We present simulation studies and an application to an infection study about the parasite Giardia lamblia among children in Kenya.The second project focuses on supervised dimension reduction. The goal of supervised dimension reduction (SDR) is to find a compact yet informative representation of the original data space via some transformation. Most SDR algorithms are formulated as an optimization problem with the objective being a linear function of the second order statistics of the data. However, such an objective function tends to overemphasize those directions already achieving large between-class distances yet making little improvement over the classification accuracy. To address this issue, we introduce two objective functions, which are directly linked to the classification accuracy, then present an algorithm that sequentially solves the nonlinear objective functions.