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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 ... 
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 ... 
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 ... 
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 ...