Involutive Metropolis proposal
= Involutive Metropolis proposal
An <involutive Metropolis proposal> uses a deterministic bijection $S$ satisfying $S^2=I$. For a volume-preserving $S$ and target <probability density function> $\rho$, accept $S(z)$ with probability $\min(1,\rho(S(z))/\rho(z))$. The identity $\rho(z)\alpha(z)=\min(\rho(z),\rho(S(z)))$ and a change of variables under $S$ prove <detailed balance>. A non-unit <Jacobian determinant> must be included when volume is not preserved.