Maximum a posteriori density estimation and the sparse grid combination technique

We study a novel method for maximum a posteriori (map) estimation of the probability density function of an arbitrary, independent and identically distributed d-dimensional data set. We give an interpretation of the map algorithm in terms of regularised maximum likelihood. We also present numerical experiments using a sparse grid combination technique and the 'opticom' method. The numerical results demonstrate the viability of parallelisation for the combination technique.