The user does not need to select the stepsize directly. Stan includes also adaptation of the step size in the warmup phase using stochastic optimization called dual averaging. The user specifies a target acceptance ratio $($in Stan actually target for expected discretization error$),$ with argument adapt$\_$delta, and a number of iterations during which adaptation of $$L$$L occurs $($warm$-$up draws$).$ Open, the interactive demo again with this link $($algorithm$=$DualAveragingNUTS, target$=$banana$),$ and adjust the Autoplay delay to around $70,$ but otherwise keep the default options, particularly, keep the target acceptance ratio $($here $)$ at $0\mathrm{.}65.$ On the top left$-$hand corner m$/$M$\_$adapt tells you how many draws have been taken compared to number of warm$-$up draws. Wait until m$/$M$\_$adapt is at least $50/200.$

$1\mathrm{.}10$: What do you observe with the first couple of iterations?

Multiple choice $10$ Question $1$

$$The algorithm initially chooses small step sizes and very few steps to quickly explore the distribution around the starting point

The algorithm initially chooses large step sizes to quickly explore the distribution

The algorithm initially chooses small step sizes and many steps to explore the distribution

$$