Details about the adapt_delta argument to rstanarm's modeling functions.

## Details

For the No-U-Turn Sampler (NUTS), the variant of Hamiltonian Monte Carlo used used by rstanarm, adapt_delta is the target average proposal acceptance probability during Stan's adaptation period. adapt_delta is ignored by rstanarm if the algorithm argument is not set to "sampling".

The default value of adapt_delta is 0.95, except when the prior for the regression coefficients is R2, hs, or hs_plus, in which case the default is 0.99.

These defaults are higher (more conservative) than the default of adapt_delta=0.8 used in the rstan package, which may result in slower sampling speeds but will be more robust to posterior distributions with high curvature.

In general you should not need to change adapt_delta unless you see a warning message about divergent transitions, in which case you can increase adapt_delta from the default to a value closer to 1 (e.g. from 0.95 to 0.99, or from 0.99 to 0.999, etc). The step size used by the numerical integrator is a function of adapt_delta in that increasing adapt_delta will result in a smaller step size and fewer divergences. Increasing adapt_delta will typically result in a slower sampler, but it will always lead to a more robust sampler.

## References

Stan Development Team. Stan Modeling Language Users Guide and Reference Manual. https://mc-stan.org/users/documentation/.

Brief Guide to Stan's Warnings: https://mc-stan.org/misc/warnings.html#divergent-transitions-after-warmup