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An Algorithmic Framework for High Dimensional Regression with Dependent Variables
(20140224)We present an exploration of the rich theoretical connections between several classes of regularized models, network flows, and recent results in submodular function theory. This work unifies key aspects of these problems ... 
Bayesian Modeling For Multivariate Mixed Outcomes With Applications To Cognitive Testing Data
(20120913)This dissertation studies parametric and semiparametric approaches to latent variable models, multivariate regression and modelbased clustering for mixed outcomes. We use the term mixed outcomes to refer to binary, ordered ... 
Bayesian Modeling of Health Data in Space and Time
(20130225)In recent years spatialtemporal modeling has become increasingly popular in the field of public health and epidemiology. Motivated by two datasets, we address three issues in the Bayesian modeling of health data in space ... 
Bayesian Nonparametric Inference of Effective Population Size Trajectories from Genomic Data
(20130725)Phylodynamics is an area at the intersection of phylogenetics and population genetics that aims to reconstruct population size trajectories from genetic data. Phylodynamic methods rely on a standard framework based on the ... 
Bayesian Population Reconstruction: A Method for Estimating Age and Sexspecific Vital Rates and Population Counts with Uncertainty from Fragmentary Data
(20130723)Current methods for reconstructing human populations of the past by age and sex are deterministic or do not formally account for measurement error. I propose “Bayesian reconstruction”, a method for simultaneously estimating ... 
Bayesian spatial and temporal methods for public health data
In this thesis, we develop flexible models to analyze public health data in time and/or in space. The development of our methodology is motivated by two examples: cancer incidence data in Washington State and birth outcome ... 
Bayesian spatial and temporal methods for public health data
In this thesis, we develop flexible models to analyze public health data in time and/or in space. The development of our methodology is motivated by two examples: cancer incidence data in Washington State and birth outcome ... 
CoordinateFree Exponential Families on Contingency Tables
(20120913)We propose a class of coordinatefree multiplicative models on the set of positive distributions on contingency tables and on some sets of cells of a more general structure. The models are called relational and are generated ... 
Degeneracy, Duration, and Coevolution: Extending Exponential Random Graph Models (ERGM) for Social Network Analysis
We address three aspects of statistical methodology in the application of Exponential family Random Graphs to modeling social network processes. The first is the topic of model degeneracy in ERGMs. We show this is a ... 
Detecting and extracting complex patterns from images and realizations of spatial point processes
(2000)A common goal in the field of Computer Vision is the detection and extraction of patterns (e.g. lines, object boundaries) from binary image data . These images routinely occur as the product of edge detection algorithms, ... 
DiscreteTime Threshold Regression for Survival Data with TimeDependent Covariates
A natural approach to survival analysis in many settings is to model the subject's ``health'' status as a latent stochastic process, where the terminal event is represented by the first time that the process crosses a ... 
Estimating Population Size Using the Network Scale Up Method
(20130725)We develop methods for estimating hardtoreach populations from data collected using networkbased questions on standard surveys. Such data arise by asking respondents how many people they know in a specific group (e.g. ... 
Functional Quantitative Genetics and the Missing Heritability Problem
In classical quantitative genetics, the correlation between the phenotypes of individuals with unknown genotypes and a known pedigree relationship is expressed in terms of probabilities of IBD states. In existing models ... 
Generalization of boosting algorithms and applications of Bayesian inference for massive datasets
(1999)In recent years statisticians, computational learning theorists, and engineers have developed more advance techniques to learn complex nonlinear relationships from datasets. However, not only have models increased in ... 
Generalized linear mixed models: development and comparison of different estimation methods
(2002)The use of generalized linear mixed models is growing in popularity in the modelling of correlated data. To date, methods available are either computationally intensive or asymptotically biased. The following work examines ... 
Genetic restoration on complex pedigrees
(1990)Analyses of genetic data observed on groups of related individuals frequently require the computation of probabilities on pedigrees. Existing methods are computationally intensive and can be infeasible on large and complex ... 
Gravimetric Anomaly Detection using Compressed Sensing
We address the problem of identifying underground anomalies (e.g. holes) based on gravity measurements. This is a theoretically wellstudied yet difficult problem. In all except a few special cases, the inverse problem has ... 
Latent models for crosscovariance
(2001)Crosscovariance problems arise in the analysis of multivariate data that can be divided naturally into two blocks of variables, X and Y, observed on the same units. In a crosscovariance problem we are interested, not in ... 
Learning and Manifolds: Leveraging the Intrinsic Geometry
(20130723)In this work, we explore and exploit the use of differential operators on manifolds  the LaplaceBeltrami operator in particular  in learning tasks. In particular, we are interested in uncovering the geometric structure ... 
The Likelihood Pivot: Performing Inference with Confidence
Maximum likelihood estimation is a popular statistical method. To account for possible model misspecification, the sandwich estimate of variance can be used to generate asymptotically correct confidence intervals. Several ...