Many practical modeling problems involve discrete data that are best represented as draws from multinomial or categorical distributions. For example, nucleotides in a DNA sequence, children's names in a given state and year, and text documents are all commonly modeled with multinomial distributions. In all of these cases, we expect some form of dependency between the draws: the nucleotide at one position in the DNA strand may depend on the preceding nucleotides, children's names are highly correlated from year to year, and topics in text may be correlated anddynamic. These dependencies are not naturally captured by the typical Dirichlet-multinomial formulation. Here, we leverage a logistic stick-breaking representation and recent innovations in Pólya-gamma augmentation to reformulate themultinomial distribution in terms of latent variables with jointly Gaussian likelihoods, enabling us to take advantage of a host of Bayesian inference techniques forGaussian models with minimal overhead.

Recent increase in interest in using rotorcraft (helicopters and tilt-rotor craft) for public transportation has spurred research in making rotorcraft less noisy, particularly as they land. The ground noise associated with landing trajectories followed by rotorcraft depends in part on the changes in altitude and velocity of the rotorcraft during flight. Acoustic models of ground noise taking altitude and velocity effects into account can be used in an optimization process to determine a set of potentially quieter pilot operations. However, optimizing solely for acoustic properties produces patterns that abstract away from the environment in which the trajectory is flown. A quiet procedure flown over a residential area can create considerable annoyance. To overcome this limitation of acoustic-based optimization we propose a hybrid cost model for optimization that combines acoustic criteria with a land use model that views noise-sensitive areas around landing facilities as weighted obstacles. The result is a 3D route planning problem with obstacles. We introduce a system, called NORA (Noise Optimization for Rotorcraft Approach) that allows for the computation of trajectories that simultaneously solve for acoustically quiet patterns that also avoid land sensitive areas.

Sampling inference methods are computationally difficult to scale for many models in part because global dependencies can reduce opportunities for parallel computation. Without strict conditional independence structure among variables, standard Gibbs sampling theory requires sample updates to be performed sequentially, even if dependence between most variables is not strong. Empirical work has shown that some models can be sampled effectively by going Hogwild'' and simply running Gibbs updates in parallel with only periodic global communication, but the successes and limitations of such a strategy are not well understood. As a step towards such an understanding, we study the Hogwild Gibbs sampling strategy in the context of Gaussian distributions. We develop a framework which provides convergence conditions and error bounds along with simple proofs and connections to methods in numerical linear algebra. In particular, we show that if the Gaussian precision matrix is generalized diagonally dominant, then any Hogwild Gibbs sampler, with any update schedule or allocation of variables to processors, yields a stable sampling process with the correct sample mean. "