Stan Implementation Details

Speed of the propto argument

The log density function provided by a Stan model has the ability to drop additive constants from the calculation. This is indicated by the propto (”proportional to”) argument to function.

If you are using an application such as an MCMC algorithm which requires gradients and only needs the log density up to a proportion, setting propto=True will be at least as fast as setting propto=False and is generally recommended (and the default value).

However, in the case of the log_density function (which does not calculate derivatives), this argument has the potential to slow down computation, and we recommend setting it to False or timing it for your model of interest before proceeding. Note that the default value of propto is True for consistency with the versions of the function that do calculate gradients, so extra care is needed.

Why is log_density different?

The implementation of the propto argument relies on the presence of autodiff types (vars, in the terminology of Stan’s math library) to determine what is or is not constant with respect to the parameters. When the argument is False, the calculation of the log density is able to be computed using only variables of type double.

The consequence of this is that, if the propto argument is set to true, the log_density function will at a minimum need to perform more allocations than if it were set to false. There may be an even higher cost, due to functions such as reduce_sum or Stan’s ODE integraters changing their behavior when applied to autodiff types and performing additional work which is thrown away when gradients are not needed. These additional computations can quickly overwhelm any speed up received by dropping additive constants in practice.