Other interfaces

Scope

Draws from identical CmdStan settings, and each interface's own summary: mean, standard deviation, 5% and 95% quantiles, R-hat, and bulk ESS for mu, tau, and theta.

References

Reference

cmdstanr 0.9.0 with posterior 1.7.0, and CmdStanPy 1.3.0 (summary at sig_figs 12), on CmdStan 2.40.0, R 4.6.2, Python 3.14.10, and PHP 8.5.12

Versions

CmdStan 2.40.0, CmdStanPHP v0.1.2-35-gccadda9, cmdstanr 0.9.0, posterior 1.7.0, cmdstanpy 1.3.0, R 4.6.2 (2026-10-29), Python 3.14.10, PHP 8.5.12

Data

Values

{"J":8,"y":[28,8,-3,7,-1,1,18,12],"sigma":[15,10,16,11,9,11,10,18]}

Arguments

chains 4; parallel chains 4; chain ids 1, 2, 3, 4; iter warmup 1000; iter sampling 1000; seed 20261101; init 2; other CmdStan's defaults for everything else, including NUTS with the diag_e metric, adapt_delta 0.8, max_treedepth 10, and the CSV output precision

data {
  int<lower=0> J;
  array[J] real y;
  array[J] real<lower=0> sigma;
}
parameters {
  real mu;
  real<lower=0> tau;
  vector[J] theta_tilde;
}
transformed parameters {
  vector[J] theta = mu + tau * theta_tilde;
}
model {
  mu ~ normal(0, 5);
  tau ~ cauchy(0, 5);
  theta_tilde ~ normal(0, 1);
  y ~ normal(theta, sigma);
}

Method

The non-centered eight schools model (Rubin 1981) run through three CmdStan interfaces with the same CmdStan, data, seed, chain ids, and initialization. The draws are identical, and each interface summarizes them with its own code.

Check

Comparison with a reference implementation

Recorded

2026-11-01, PHP 8.5.12, Ubuntu 24.04.5 LTS (x86_64), commit ccadda9

Tolerances

x: package value; r: reference value. Absolute error: |x − r|. Max errors are over the values a row compares. cmdstanr, CmdStanPy: each implementation’s error against the same reference.

Results

61 comparisons in 11 cases: 61 pass, 0 fail, 0 skipped.

By case

Posterior means by interface

• CmdStanPHP: summary() with measures mean, sd, quantile2, rhat, and ess_bulk
• cmdstanr: fit$summary() (posterior package): mean, sd, quantile 0.05 and 0.95, rhat, ess_bulk
• CmdStanPy: fit.summary(percentiles=(5, 95)), which runs CmdStan's stansummary: Mean, StdDev, 5%, 95%, R_hat, ESS_bulk

Values to six decimal places; the signed number is the difference from CmdStanPHP's unrounded mean.

Draws

Summaries

CmdStanPHP's and cmdstanr's summaries agree to rounding error in double precision. CmdStanPy's summary() rounds stansummary's output to 6 significant figures by default, which accounts for its differences. With summary(sig_figs=12), its largest differences are those in summary_differences_cmdstanpy_sig_figs_12.

Limitations

Known differences

• CmdStanPy's summary() rounds stansummary's output to 6 significant figures by default, so its summary is compared at sig_figs 12.

Reproduction

verification/interfaces/run.sh

Raw record

site/verifications/interfaces.json

Full results

verification/interfaces