= Centered polynomial birth move in reversible-jump sampling
{title2=$\beta'_0=\beta_0-cz$}
A <polynomial regression> birth move can introduce a coefficient $z$ while shifting the intercept by $-cz$, with $c$ the sample average of the new monomial. The fitted-value increment is $z(x^{k+1}-c)$, whose sample average vanishes. The <Jacobian determinant> of the coefficient transformation is one. A <reversible-jump Markov chain Monte Carlo> acceptance ratio must still include the normalized dimension-dependent <prior distributions>, the model-order <prior distribution>, the birth/death selection probabilities and the proposal density for $z$.
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