%0 Journal Article %A Hollister, Brad Eric %A Pang, Alex %D 2015 %I Begell House %K spatial statistics, density estimation, computational statistics, random fields, uncertainty quantification, representation of uncertainty, spatial uncertainty %N 2 %P 123-137 %R 10.1615/Int.J.UncertaintyQuantification.2015011789 %T BIVARIATE QUANTILE INTERPOLATION FOR ENSEMBLE DERIVED PROBABILITY DENSITY ESTIMATES %U https://www.dl.begellhouse.com/journals/52034eb04b657aea,65319583582efa6d,2351b1ed401f87be.html %V 5 %X 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. %8 2015-05-07