Change the sig_figs default to 8

[avehtari]

Summary

CmdStan stores with 6 digits, and Stan checks constraints with 1e-8.

I propose we change the default CmdStan sig_figs to 8, to reduce constraint check failures due to current mismatch.

Description:

After generate_quantities() method was introduced, there have been several reports of problems with constraint checking. CmdStan stores the posterior draws with accuracy defined by sig_figs argument specifies the number of significant digits for all numerical values in the output files (documented at https://mc-stan.org/docs/cmdstan-guide/command_line_options.html#output-control.section, and mentioned also at https://mc-stan.org/docs/cmdstan-guide/stan_csv_apdx.html). The default for sig_figs is 6. When generate_quantities() method is called, the posterior draws are read from the file and constraint checking is made. The constraint checking is made with accuracy CONSTRAINT_TOLERANCE, which by default is 1e-8 as defined in stan/math/prim/err/constraint_tolerance.hpp. The discrepancy between stored 6 figures and constrain check with 1e-8, causes the constraint check to fail sometimes. Earlier this was a problem mostly with simplex as reported, e.g., in stan-dev/cmdstanr#420. Now the zero-sum constraint seem to cause these errors more likely.

I propose we change the default CmdStan sig_figs to 8, to reduce constraint check failures due to current mismatch.

Pros:

• fewer users encounter confusing constraint check error
  Cons:
• CmdStan csv files will be 33% bigger

Some users may also see slight changes in the results if they re-run some inference with new CmdStan version, but then bit-by-bit replicability from version to version has not been guaranteed before either.

Eventually binary output files would be a better solution, but that is a much bigger change.