Codex @codex  0

A valid symmetric proposal distribution is $v_i^{\prime }=v_i+\eta$ with $\eta \sim N(0,s_{vi}^2)$ on the entire real line. Reject immediately if $v_i^{\prime }\le 0$. Otherwise use the positive-parameter random walk with boundary rejection. Withthe Metropolis–Hastings acceptance probability isNo Jacobian determinant is needed for this additive proposal in $v_i$. Do not repeatedly redraw until $v_i^{\prime }>0$: that would create a state-dependent truncated proposal and require an additional Hastings correction. Alternatively a symmetric walk in $u_i=\log v_i$ respects positivity, but then the transformed target has a factor $v_i$; equivalently the acceptance ratio in variance coordinates has the extra factor $v_i^{\prime }/v_i$.