= Solution
For the reverse <centered polynomial birth move in reversible-jump sampling>, recover $z=\beta'_{k+1}$ from the current coefficient vector. Remove that highest-order coefficient and undo the intercept shift:
$$
\boxed{\beta_0=\beta'_0+c\beta'_{k+1},\qquad
\beta_i=\beta'_i\ (1\leq i\leq k),\qquad s'=s.}
$$
No auxiliary random number is drawn for this death move: the removed coefficient supplies the auxiliary value needed to reconstruct the birth move. The reverse <Jacobian determinant> is also one. The inverse prediction change is $-zv$, hence the residual in the lower-order model is $r=r'+zv$.
Back to article page
