The best SBC results for Stan's algorithm uses a uncentered parameterisation of SV. The rank stats appear uniform across all static parameters. Kim et al's bespoke algorithm performed best on a centered SV. But their rank statistics are less uniform and therefore less calibrated.

SV is expressed as a state space model - there is a latent conditional variance to be estimated for each data point (which means k parameters > n observations). For brevity I'll show the SBC results for only the static parameters (mu, phi, sigma).

Talts et al (2020) prove the rank statistics from a calibrated analysis is uniformly distributed. If rank statistics has a large left peak, then the avg posterior is overestimating the prior. Two peaks on either side suggests under dispersion relative to the prior.

The true parameter in SBC is a sample from the prior dist. Calibration also implies the posterior averaged over the data and true parameters equals the prior. Therefore, if MCMC is calibrated, rank stats should be uniform which implies the avg posterior equals the prior.

SBC runs many simulations and checks if the rank statistics (definition in slides) of each parameter follow a uniform distribution. A calibrated analysis means that the correct posterior estimate is returned _on average_ over these simulations.

This is a good check that the model and code is working as expected. However, results form a single simulation are insufficient. There is a small chance the true parameter (solid vertical line) exists in the tails of the marginal posterior distribution (phi).

I can summarise how I learn things with a single comic, especially as a new parent:

Source: www.facebook.com/webcomicname...