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Metropolis-Hastings Proposal Distribution multiplied by scalar. How does this affect the Hastings Ratio?

$begingroup$ This question was migrated from Stack Overflow because it can be answered on Cross Validated. Migrated 16 days ago. So, if I propose $theta^*$ from $text{Dirichlet}(theta_i times tau)$, where $tau$ is some scalar, does the Metropolis-Hastings atio need to account for that scalar i.e. $$text{Dirichlet}(theta_i|theta^*timestau) big/ text{Dirichlet}(theta^*|theta_i timestau)$$ or should I drop the $tau$‘s […]