RT Journal Article ID 2351b1ed401f87be A1 Hollister, Brad Eric A1 Pang, Alex T1 BIVARIATE QUANTILE INTERPOLATION FOR ENSEMBLE DERIVED PROBABILITY DENSITY ESTIMATES JF International Journal for Uncertainty Quantification JO IJUQ YR 2015 FD 2015-05-07 VO 5 IS 2 SP 123 OP 137 K1 spatial statistics K1 density estimation K1 computational statistics K1 random fields K1 uncertainty quantification K1 representation of uncertainty K1 spatial uncertainty AB 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. PB Begell House LK https://www.dl.begellhouse.com/journals/52034eb04b657aea,65319583582efa6d,2351b1ed401f87be.html