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.

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