# Default initial step size

What is the default initial step size used by:

• RStan (element stepsize in the control argument of rstan::stan())?
• CmdStan (and therefore also by CmdStanR, argument step_size of the \$sample() method for CmdStanModel objects)?

I can’t find these default values in the corresponding docs. The only document I’ve found is this one where a value of 2.0 is mentioned, but that document only seems to refer to RStan. In the CmdStan source code, a value of 1 seems to be used, but I’m not sure if I’m interpreting the source code correctly.

Hi,

I assume they use the default values Stan uses?

i.e., \delta=0.8, \gamma=0.05, \kappa=0.75, and t_0 = 10. Is this what you were after?

There’s is no default stepsize per se, but only default method to initialize stepsize, which you can find in NUTS paper. The gist is to come up a stepsize that makes the acceptance probability above given threshold. The actual value of initial stepsize varies by random seed. The code you are looking for is init_stepsize in base_hmc.hpp.

EDIT: I changed the category to “algorithm”.

Thanks a lot for your replies.

First, I’m sorry because I didn’t realize that there is a special CmdStan Guide. There, on page 56, it explicitly says that the default value for stepsize is 1. Then I guess this default is also used for RStan?

Secondly, I think I understood @yizhang’s explanation. However, what is then the purpose of this argument stepsize (or step_size in CmdStanR)? My whole question arose in the first place because I was getting several informational messages by CmdStanR saying

Scale parameter is inf, but must be finite!


and I realized that I can get rid of these by lowering the step_size value to 0.1, as proposed here.

What’s given to step_size arg is exactly for init_stepsize, a starting point to find a proper stepsize for adaptation to get to proper acceptance probability. That step_size defaults to 1(cmdstan user guide), and reducing it makes it easier to reach that acceptance probability(so you don’t see those warnings anymore). Just keep in mind that step_size is not the actual stepsize the adaptation uses in the first warmup iteration.

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Alright, thanks.

This is correct. Note also that if step_size is small enough then the step size initialization routine will immediately pass and sampling will start with a smaller step size than what the initialization routine would have found even if it had worked, so it can be a helpful way to facilitate warmup in difficult problems.

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I forgot to ask again for the default value used by RStan: Is this also 1 (in contrast to this document already mentioned above)?

Yes it’s 1 by default, as it’s basically cmdstan specification. See https://mc-stan.org/docs/2_23/cmdstan-guide/mcmc-config.html#hmc-samplers

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This is missing from the RStan doc, so I created an issue to add it there:

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