Algorithm 2 Metropolis–Hastings sampling.

$x\sim p_0(x)$   repeat      $x^{\prime }\sim p_0(x^{\prime })$       $u\sim \mathrm{Uniform}[0,1]$       if $u\le \exp (\beta (\Delta U(x^{\prime })-\Delta U(x)))$ then accept $x\leftarrow x^{\prime }$   until chain has converged to equilibrium return x