arXiv subjects

Luke Bornn

Publications and source records attributed to Luke Bornn.

39 records · Page 3Linked to original sources

arXiv2011

Modeling Non-Stationary Processes Through Dimension Expansion

In this paper, we propose a novel approach to modeling nonstationary spatial fields. The proposed method works by expanding the geographic plane over which these processes evolve into higher dimensional spaces, transforming and clarifying complex patterns in the physical plane. By combining aspects of multi-dimensional scaling, group lasso, and latent variables models, a dimensionally sparse projection is found in which the originally nonstationary field exhibits stationarity. Following a comparison with existing methods in a simulated environment, dimension expansion is studied on a classic test-bed data set historically used to study nonstationary models. Following this, we explore the use of dimension expansion in modeling air pollution in the United Kingdom, a process known to be strongly influenced by rural/urban effects, amongst others, which gives rise to a nonstationary field.

stat.ME↗

arXiv2010

Discussion of "Riemann manifold Langevin and Hamiltonian Monte Carlo methods'' by M. Girolami and B. Calderhead

This technical report is the union of two contributions to the discussion of the Read Paper "Riemann manifold Langevin and Hamiltonian Monte Carlo methods" by B. Calderhead and M. Girolami, presented in front of the Royal Statistical Society on October 13th 2010 and to appear in the Journal of the Royal Statistical Society Series B. The first comment establishes a parallel and possible interactions with Adaptive Monte Carlo methods. The second comment exposes a detailed study of Riemannian Manifold Hamiltonian Monte Carlo (RMHMC) for a weakly identifiable model presenting a strong ridge in its geometry.

stat.CO↗

arXiv2010

Grouping Priors and the Bayesian Elastic Net

In the literature surrounding Bayesian penalized regression, the two primary choices of prior distribution on the regression coefficients are zero-mean Gaussian and Laplace. While both have been compared numerically and theoretically, there remains little guidance on which to use in real-life situations. We propose two viable solutions to this problem in the form of prior distributions which combine and compromise between Laplace and Gaussian priors, respectively. Through cross-validation the prior which optimizes prediction performance is automatically selected. We then demonstrate the improved performance of these new prior distributions relative to Laplace and Gaussian priors in both a simulated and experimental environment.

stat.ME↗