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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 ... 
The weighted likelihood bootstrap and an algorithm for prepivoting
(1991)The method of bootstrapping, which has transformed the theory and practice of frequentist statistical inference, is applicable within the Bayesian paradigm. Rather than simulating data that might have been observed, this ... 
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 ... 
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 ... 
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, ... 
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 ... 
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 ... 
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 ... 
Robust estimation of factor models in finance
(2005)Standard assetpricing models entail expressions for expected returns in terms of coefficients relative to risk factors. Methods to estimate premiums of risk factors have, at its core, a single or multiple linear regression ... 
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 ... 
A resampling approach to clustering with confidence
(20120913)We propose a method for estimating the number of groups in a data set. Our method is an extension of Generalized Single Linkage clustering (GSL) (Stuetzle and Nugent 2010), a nonparametric clustering method based on the ... 
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 ... 
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 ... 
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 ... 
Tests for Differences between Least Squares and Robust Regression Parameter Estimates and Related Topics
(20130417)At the present time there is no well accepted test for comparing least squares and robust linear regression coefficient estimates. To fill this gap we propose and demonstrate the efficacy of two Waldlike statistical tests ... 
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 ... 
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 ... 
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 ... 
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. ... 
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 ...