Optimal approximation

Optimal Belief Approximation

In Bayesian statistics probability distributions express beliefs. However, for many problems the beliefs cannot be computed analytically and approximations of beliefs are needed. We seek a ranking function that quantifies how “embarrassing” it is to communicate a given approximation. We show that there is only one ranking under the requirements that (1) the best ranked approximation is the non-...

Optimal Approximation on

The theory of functions on the two-dimensional sphere was initiated in the 18th century in the works of Laplace and Legendre. The general theory for the d-dimensional sphere was started at the beginning of this century. Due to the technical difficulties involved, the general theory is relatively incomplete, as compared to the theory of functions on the circle. We are introducing a wide range of...

Optimal Approximation of Functions

Optimal Approximation of Signal Priors

In signal restoration by Bayesian inference, one typically uses a parametric model of the prior distribution of the signal. Here, we consider how the parameters of a prior model should be estimated from observations of uncorrupted signals. A lot of recent work has implicitly assumed that maximum likelihood estimation is the optimal estimation method. Our results imply that this is not the case....

Approximation of optimal stopping problems

We consider optimal stopping of independent sequences. Assuming that the corresponding imbedded planar point processes converge to a Poisson process we introduce some additional conditions which allow to approximate the optimal stopping problem of the discrete time sequence by the optimal stopping of the limiting Poisson process. The optimal stopping of the involved Poisson processes is reduced...