Curved factor analysis with the Ellipsoid-Gaussian distribution

Abstract

There is a need for new models for characterizing dependence in multivariate data. The multivariate Gaussian distribution is routinely used, but cannot characterize nonlinear relationships in the data. Most non-linear extensions tend to be highly complex; for example, involving estimation of a non-linear regression model in latent variables. In this article, we propose a relatively simple class of Ellipsoid-Gaussian multivariate distributions, which are derived by using a Gaussian linear factor model involving latent variables having a von Mises-Fisher distribution on a unit hyper-sphere. We show that the Ellipsoid-Gaussian distribution can flexibly model curved relationships among variables with lower-dimensional structures. Taking a Bayesian approach, we propose a hybrid of gradient-based geodesic Monte Carlo and adaptive Metropolis for posterior sampling. We derive basic properties and illustrate the utility of the Ellipsoid-Gaussian distribution on a variety of simulated and real data applications.

Limits of epidemic prediction using SIR models

“…where Λ = R T A −1 with c, A, and R as in (1.1), η i ∼ vMF(µ, τ) are independent random variables drawn from the von Mises-Fisher distribution on S p−1 , and i ∼ N p (0, σ 2 I) are independent multivariate normal random variables representing noise. Model (3.1) is introduced and studied in detail in [25]. The parameters of vMF(µ, τ) are the mean µ ∈ S p−1 and measure of spread τ 0.…”