BIVARIATE QUANTILE INTERPOLATION FOR ENSEMBLE DERIVED PROBABILITY DENSITY ESTIMATES
Brad Eric Hollister, Alex Pang · International Journal for Uncertainty Quantification · 2015
Probability distribution functions (PDFs) may be estimated from members in an ensemble.For an ensemble of 2D vector fields, this results in a bivariate PDF at each location in the field.Vector field analysis and visualization, e.g., stream line calculation, require an interpolation to be defined over these 2D density estimates.Thus, a nonparametric PDF interpolation must advect features as opposed to cross-fading them, where arbitrary modalities in the distribution can be introduced.This is already achieved for 1D PDF interpolation via inverse cumulative distribution functions (CDFs).However, there is no closed-form extension to bivariate PDF.This paper presents one such direct extension of the 1D closed-form solution for bivariates.We show an example of physically coupled components (velocity) and correlated random variables.Our method does not require a complex implementation or expensive computation as does displacement interpolation Bonneel et al., ACM Trans.Graphics (TOG), 30(6):158, 2011.Additionally, our method does not suffer from ambiguous pair-wise linear interpolants, as does Gaussian Mixture Model Interpolation.