We discussed setting a default number of MCMC samples per calibration, possibly using mixing information from the long MCMC run (integrated autocorrelation time).
If I have a target ESS of 200 for the short chain, estimating the integrated autocorrelation time from the long chain would give me a ballpark estimate of the number of MCMC samples needed to reach an ESS of 200. If $\tau$ is the integrated autocorrelation time
$$\tilde{m} = \text{ESS}_{\text{target}} \times \tau$$
The chain we want to monitor is the difference between the discrepancy for the posterior predictive and the observed discrepancy, i.e., D(y_rep, θ) - D(y_obs, θ).
Open question: with multiple discrepancies, do we estimate $\tau$ per discrepancy and take the max (most conservative), or pick one some other way?
@abigailkeller I think this was your suggestion, so tagging you in case I remember something wrong.
We discussed setting a default number of MCMC samples per calibration, possibly using mixing information from the long MCMC run (integrated autocorrelation time).
If I have a target ESS of 200 for the short chain, estimating the integrated autocorrelation time from the long chain would give me a ballpark estimate of the number of MCMC samples needed to reach an ESS of 200. If$\tau$ is the integrated autocorrelation time
The chain we want to monitor is the difference between the discrepancy for the posterior predictive and the observed discrepancy, i.e.,
D(y_rep, θ) - D(y_obs, θ).Open question: with multiple discrepancies, do we estimate$\tau$ per discrepancy and take the max (most conservative), or pick one some other way?
@abigailkeller I think this was your suggestion, so tagging you in case I remember something wrong.