A Finite Element Method for Density Estimation with Gaussian Process Priors
Michael Griebel, Markus Hegland · SIAM Journal on Numerical Analysis · 2010
A variational problem characterizing the density estimator defined by the maximum a posteriori method with Gaussian process priors is derived. It is shown that this problem is well posed and can be solved with Newton's method. Numerically, the solution is approximated by a Galerkin/finite element method with piecewise multilinear functions on uniform grids. Error bounds for this method are given and numerical experiments are performed for one-, two-, and three-dimensional examples.