# Calculation of Exact Estimators via n-Dimensional Spherical Surface Integrals

## Calculation of Exact Estimators via n-Dimensional Spherical Surface Integrals

Calculation of Exact Estimators via n-Dimensional Spherical Surface Integrals 150 150 UKAEA Opendata

# Calculation of Exact Estimators via n-Dimensional Spherical Surface Integrals

This paper reconsiders the problem of calculating the expected set of probabilities hpii, given the observed set of items {mi}, that are distributed among n bins with an (unknown) set of probabilities {pi} for being placed in the ith bin. The problem is often formulated using Bayes theorem and the multinomial distribution, that with a constant prior for the values of the pi, leads to a Dirichlet distribution for the {pi}. Here the moments are calculated by a change of variables that reduces the problem to an integration over a portion of the surface of an n-dimensional sphere.

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01/02/2012