Orthogonal-mixture Metropolis proposal
= Orthogonal-mixture Metropolis proposal
For a proposal $Y=AX+Z$, with isotropic $Z\sim N(0,I)$ and an independent random <orthogonal matrix> $A$, invariance of the distribution of $A$ under transpose makes the <proposal distribution> symmetric. Indeed $|y-Ax|=|x-A^Ty|$, and averaging the isotropic Gaussian density over an inversion-invariant law yields $q(x,y)=q(y,x)$. The <Metropolis–Hastings algorithm> therefore accepts with the target density ratio alone.