The illegal slaughter of African elephants for ivory is now worse than it was at its peak in the
1980s. The most effective way to contain this illegal trade is to determine where poaching is occurring.
Two Bayesian methods, Voronoi and SCAT, can be used to simultaneously map elephant populations
over the entire African continent and determine the geographic origin(s) of poached elephant ivory using
genetic data. I will present some results of these methods applied to a large volume contraband seizure
from Singapore and illustrate the genetic implications of poaching.

Biology is increasingly moving beyond an atomistic, single-protein or single-gene scope to work on a systems level, examining the behavior of biological networks.  Modern high-dimensional data allow quick estimation of network structures that before would have required years of work in the lab.  We propose the Joint Graphical Lasso, a method for estimation of biological networks across multiple classes of data, for example in cancer and normal tissue.  I will review the principles of network estimation, introduce our proposal for extending estimation to multiple classes of data, describe its solution using convex optimization, and describe analyses of real and simulated datasets. 
Keywords: graphical lasso, networks, gene expression, penalized likelihood, gradient descent

Comparing rates of change across groups is a natural use of longitudinal data as a common purpose for collecting such data is to understand how the outcome changes over time.  A standard approach to comparing rates across groups is to use a linear mixed effects model with a group by time interaction.  However, in the presence of a non-linear trend in the outcome, this approach may not be sufficient.  Other existing approaches are typically designed for specific applications and are not easily generalizable.  Thus, we propose methodology for longitudinal outcomes that allow for comparing rates of change across groups under the presence of a non-linear trend over time.  Our rate regression method assumes a proportional change in the rate at every point in time across groups defined by a covariate of interest.  Simulation results have demonstrated gains in power of the rate regression model in comparison to a linear mixed effects model under the presence of a non-linear trend in time.  Possible areas of application for the proposed method include research in child and adolescent development and treatment trials.  Numerous possible extensions to the rate regression method also exist such as in methods for multivariate longitudinal data and semiparametric methods for estimating a generalized time trend.

Various methods, with corresponding assumptions, exist for estimating graphical models in the multivariate Gaussian case. Two such methods are the LASSO and the adaptive LASSO which require the assumptions of neighborhood stability and restricted eigenvalue, respectively. In this talk, I present the methods and results of a simulation study assessing the validity of the assumptions using three different network generation models (Erdos-Renyi random graph, Watts-Strogatz rewired lattice and Barabasi-Albert preferential attachment network).

Longitudinal studies are a useful tool for investigating the course of chronic diseases.  Many chronic diseases are progressive and can be characterized by a set of health states.  We can gain a greater understanding of the disease process by modeling the sequence of visited states and the length of time spent in each state.  The major modeling challenge is that the transition times are not known exactly under panel observation.  Existing modeling approaches either impose strong parametric assumptions on the sojourn times in each state, or model time discretely and carry out inference nonparametrically, but both approaches have drawbacks.  We propose an alternative modeling approach that uses the principle of data augmentation.  This method has several advantages: (1) it accommodates any parametric model for the sojourn times, including spline models; (2) it performs well under small sample sizes for suitable parametric choices for the sojourn time distributions; and (3) it does not require that subjects be observed in every health state.  We evaluate the performance of this approach under various choices of sojourn time model and compare it to existing approaches under a sparse observation scheme.  Finally, we illustrate the proposed approach in an application and discuss future research directions.