Statistics and Probability Commons^™

Variational Inference For Quantile Rgression, Bufei Guo

Arts & Sciences Electronic Theses and Dissertations

Quantile regression (QR) (Koenker and Bassett, 1978), is an alternative to classic lin- ear regression with extensive applications in many fields. This thesis studies Bayesian quantile regression (Yu and Moyeed, 2001) using variational inference, which is one of the alternative methods to the Markov chain Monte Carlo (MCMC) in approximating intractable posterior distributions. The lasso regularization is shown to be effective in improving the accuracy of quantile regression (Li and Zhu, 2008). This thesis developed variational inference for quantile regression and regularized quantile regression with the lasso penalty. Simulation results show that variational inference is a computationally more efficient alternative …

Essays On Econometrics And Rational Choice, Junnan He

Arts & Sciences Electronic Theses and Dissertations

Decision and choice theory is a topic of interest in both econometrics and microeconomic theory. We contribute to the theory of decision under both contexts, that is, the theory of model selection in econometrics, and the theory of rational decision in microeconomics.

There is a long-lasting theoretical interest in model selection. More recently, research on sparse estimators, a class of estimation methods that select and estimate important parameters simultaneously, has been the central focus on model selection. The methods become especially relevant when the problem is of high-dimensional nature. Theoretically, sparse methods can perform well when the true data generating …

Quantifying Lithochemical Diversity Of Martian Materials Using Hierarchical Clustering And A Similarity Index For Classification, Michael Conner Bouchard

Arts & Sciences Electronic Theses and Dissertations

We are currently living in the golden age of robotic exploration of Mars, with a continued robotic presence there since 1997. Next to Earth, Mars is the planet about which we have gathered the most geologic information. Unlike Earth, Mars does not appear to have plate tectonics, and the planet’s primary and secondary crust is dominated by basalts. Understanding the compositional diversity of the materials that make up the martian crust will give us a better insight into the geologic processes that formed the planet and its subsequent evolution. One large and growing source of martian surface compositions is the …

Mechanics Of Phenotypic Aging Trajectories In C. Elegans And Humans, William Zhang

Arts & Sciences Electronic Theses and Dissertations

Overall, my dissertation integrates longitudinal measurements of physiology to investigate the aging process. In the first half, I examine the surprising and largely unexplained degree of variation in lifespan within even homogeneous populations. I sought to understand how physiological aging differs between long- and short-lived individuals within a population of genetically identical C. elegans reared in a homogeneous environment. Using a novel culture apparatus, I longitudinally monitored aspects of aging physiology across a large population of isolated individuals. Aggregating several measures into an overall estimate of senescence, I find that long- and short-lived individuals start adulthood on an equal physiological …

Topics In Complex And Large-Scale Data Analysis, Guanshengrui Hao

Arts & Sciences Electronic Theses and Dissertations

Past few decades have witnessed skyrocketed development of modern technologies. As a result, data collected from modern technologies are evolving towards a direction with more complicated structure and larger scale, driving the traditional data analysis methods to develop and adapt. In this dissertation, we study three statistical issues rising in data with complicated structure and/or in large scale. In Chapter 2, we propose a Bayesian framework via exponential random graph models (ERGM) to estimate the model parameters and network structures for networks with measurement errors; In Chapter 3, we design a novel network sampling algorithm for large-scale networks with community …