# Bayesian numerical analysis

Distributing points $\{x_i\}_{i=1}^n$ on the sphere as to minimize the mean square error

$\mathbb{E}\left[\left(q_n(f) - \int_{\mathbb{S}^2}f(s)\,ds\right)^2\right]$

of the quadrature formula $q_n(f) =\frac{1}{n}\sum_{i=1}^n f(x_i)$, where $f$ is a centered Gaussian process with covariance function $C(x,y) = \exp(\langle x, y \rangle)$. Shown is $n=6, 12, 23$.