Prior Distribution for the \(\mathbf{j}\)th parameter Rules for selection of parameter initial guess \({\hat{\mathbf{\theta}}}_{\mathbf{j}\mathbf{0}}\)
Case I: Informative initial guess \(N(\mu:\ \theta_{j},\ \sigma:\ s_{\theta_{j}}=\frac{1}{5}\theta_{j})\) Discard any parameter initial guesses beyond \(\theta_{j}\) \(\pm\ \)3\({s_{\theta}}_{j}\) and select again.
Case II: Moderately informative initial guess \(N(\mu:\ \theta_{j},\ \sigma:\ s_{\theta_{j}}=\frac{1}{2}\theta_{j})\) Discard any negative parameter initial guesses and any values beyond \(\theta_{j}\) \(\pm\ \)3\({s_{\theta}}_{j}\) and selected again.
Case III: Misinformed initial guess \(N(\mu:\ \theta_{j},\ \sigma:\ s_{\theta_{j}}=\frac{1}{5}\theta_{j})\) Select initial guess all from the tails of the distribution, beyond \(\theta_{j}\) \(\pm\)3 \(s_{\theta_{j}}\). Discard any negative value and select again.