Data assimilation using Bayesian filters and B-spline geological models

Bayesian data assimilation

Anti-aliasing with Stratified B-spline Filters

A simple and elegant method is presented to perform anti-aliasing in ray traced images. The method uses stratified sampling to reduce the occurrence of artifacts in an image and features a B-spline filter to compute the final luminous intensity at each pixel. The method is scalable through the specification of the filter order. A B-spline filter of order one amounts to a simple anti-aliasing sc...

Local Filters of B-spline Wavelets

Haar wavelets have been widely used in Biometrics. One advantage of Haar wavelets is the simplicity and the locality of their decomposition and reconstruction filters. However, Haar wavelets are not satisfactory for some applications due to their non-continuous behaviour. Having a particular level of smoothness is important for many applications. B-spline wavelets are capable of being applied t...

Bayesian quantile regression using random B-spline series prior

A Bayesian method for simultaneous quantile regression on a real variable is considered. By monotone transformation, the response variable and the predictor variable are transformed into the unit interval. A representation of quantile function is given by a convex combination of two monotone increasing functions ξ1 and ξ2 not depending on the prediction variables. In a Bayesian approach, a prio...

Using Low-Rank Ensemble Kalman Filters for Data Assimilation with High Dimensional Imperfect Models

Low-rank square-root Kalman filters were developed for the efficient estimation of the state of high dimensional dynamical systems. These filters avoid the huge computational burden of the Kalman filter by approximating the filter’s error covariance matrices by low-rank matrices. Accounting for model errors with these filters would cancel the benefits of the low-rank approximation as the insert...