GLOBAL RATES OF CONVERGENCE OF THE MLES OF LOG-CONCAVE AND -CONCAVE DENSITIES.

We establish global rates of convergence for the Maximum Likelihood Estimators (MLEs) of log-concave and -concave densities on ℝ. The main finding is that the rate of convergence of the MLE in the Hellinger metric is no worse than when -1 < < ∞ where = 0 corresponds to the log-concave case. We also show that the MLE does not exist for the classes of -concave densities with < -1.

Observations on abundance of bluntnose sixgill sharks, Hexanchus griseus, in an urban waterway in Puget Sound, 2003-2005.

The bluntnose sixgill shark, Hexanchus griseus, is a widely distributed but poorly understood large, apex predator. Anecdotal reports of diver-shark encounters in the late 1990's and early 2000's in the Pacific Northwest stimulated interest in the normally deep-dwelling shark and its presence in the shallow waters of Puget Sound. Analysis of underwater video documenting sharks at the Seattle Aquarium's sixgill research site in Elliott Bay and mark-resight techniques were used to answer research questions about abundance and seasonality.

Fitting Birth-Death Processes to Panel Data with Applications to Bacterial DNA Fingerprinting.

Continuous-time linear birth-death-immigration (BDI) processes are frequently used in ecology and epidemiology to model stochastic dynamics of the population of interest. In clinical settings, multiple birth-death processes can describe disease trajectories of individual patients, allowing for estimation of the effects of individual covariates on the birth and death rates of the process. Such estimation is usually accomplished by analyzing patient data collected at unevenly spaced time points, referred to as panel data in the biostatistics literature.