This dissertation studies parametric and semiparametric approaches to latent variable models, multivariate regression and model-based clustering for mixed outcomes. We use the term mixed outcomes to refer to binary, ordered ...

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 ...

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 ...

We propose a class of coordinate-free 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 ...

We develop methods for estimating hard-to-reach populations from data collected using network-based questions on standard surveys. Such data arise by asking respondents how many people they know in a specific group (e.g. ...

In recent years statisticians, computational learning theorists, and engineers have developed more advance techniques to learn complex non-linear relationships from datasets. However, not only have models increased in ...

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 ...

Cross-covariance 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 cross-covariance problem we are interested, not in ...

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 ...

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 ...