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Latent Variable Models for Indirectly or Imprecisely Measured Networks
In many scientific settings, networks are important structures used to represent the relationships between actors in a population of study. The most common methods for measuring networks are to survey study participants ... 
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 ... 
LikelihoodBased Inference for Partially Observed MultiType Markov Branching Processes
Markov branching processes are a class of continuoustime Markov chains (CTMCs) frequently used in stochastic modeling with ubiquitous applications. Bivariate or multitype processes are necessary to model phenomena such ... 
Linear Structural Equation Models with NonGaussian Errors: Estimation and Discovery
Linear structural equation models (SEMs) are multivariate models which encode direct causal effects. We focus on SEMs in which unobserved latent variables have been marginalized and only observed variables are explicitly ... 
Lord's Paradox and Targeted Interventions: The Case of Special Education
Lord (1967) describes a hypothetical “paradox” in which two statisticians, analyzing the same dataset using different but defensible methods, come to very different conclusions about the effects of an intervention on student ... 
Maximum likelihood estimation in Gaussian AMP chain graph models and Gaussian ancestral graph models
(2004)Graphical Markov models use graphs to represent dependencies between stochastic variables. Via Markov properties, missing edges in the graph are translated into conditional independence statements, which, in conjunction ... 
Methods for estimation and inference for highdimensional models
This thesis tackles three different problems in highdimensional statistics. The first two parts of the thesis focus on estimation of sparse highdimensional undirected graphical models under nonstandard conditions, ... 
Metric Learning for Hermitian Manifolds
In recent years, manifold learning has emerged as one of the most promising approaches for performing nonparametric dimension reduction. While numerous manifold learning algorithms of varying degrees of complexity have ... 
ModelBased Penalized Regression
This thesis contains three chapters that consider penalized regression from a modelbased perspective, interpreting penalties as assumed prior distributions for unknown regression coefficients. In the first chapter, we ... 
Modeling Heterogeneity within and between Matrices and Arrays
(20131114)Datasets in the form of matrices and arrays arise frequently in the social and biological sciences and are characterized by measurements indexed by two or more factors. In this dissertation we address two problems relating ... 
Monte Carlo estimation of identity by descent in populations
Genetic similarity between organisms arises from segments of shared genome, which are said to be identical by descent (IBD). Modeling IBD in pedigrees forms the basis of classical linkage analysis and has been a fruitful ... 
Monte Carlo likelihood calculation for identity by descent data
(1999)Two individuals are identical by descent at a genetic locus if they share the same gene copy at that locus due to inheritance from a recent common ancestor. Identity by descent can be thought of as a continuous process ... 
NonGaussian Graphical Models: Estimation with Score Matching and Causal Discovery under ZeroInflation
Graphical models specify conditional independence relations between variables. These include undirected graphical models and directed graphical models, the latter of which also capture causal relationships. This dissertation ... 
Nonparametric inference on monotone functions, with applications to observational studies
In this dissertation, we study general strategies for constructing nonparametric monotone function estimators in two broad statistical settings. In the first setting, a sensible initial estimator of the monotone function ... 
Parameter Identification and Assessment of Independence in Multivariate Statistical Modeling
We are interested in the extent to which, possibly causal, relationships can be statistically quantified from multivariate data obtained from a system of random variables. In the ideal setting, we would begin with refined ... 
Phylogenetic Stochastic Mapping
Phylogenetic stochastic mapping is a method for reconstructing the history of trait changes on a phylogenetic tree relating species/organisms carrying the trait. Stateoftheart methods assume that the trait evolves ... 
Portfolio Optimization with Tail Risk Measures and NonNormal Returns
(20100820)The traditional Markowitz meanvariance portfolio optimization theory uses volatility as the sole measure of risk. However, volatility is flawed both intuitively and theoretically: being symmetric it does not differentiate ... 
Predictive Modeling of Cholera Outbreaks in Bangladesh
Despite seasonal cholera outbreaks in Bangladesh, little is known about the relationship between environmental conditions and cholera cases. We seek to develop a predictive model for cholera outbreaks in Bangladesh based ... 
Preferential sampling and model checking in phylodynamic inference
Estimating population size fluctuations is one of the key tasks in Ecology. Traditional sampling based approaches to this task have limitations when populations of interest are extinct or are hard to reach, as is the case ...