Figures

CmdStanPHP draws the bayesplot diagnostics most used with MCMC: traces, histograms, densities, intervals, rank histograms, scatter plots, autocorrelation, and loo’s Pareto k plot. The statistics are computed in PHP, so figures need no R and no JavaScript to compute.

$density = CmdStan\mcmc_dens($fit, 'theta');
echo $density->ascii(60, 10), "\n";
echo CmdStan\mcmc_intervals($fit)->ascii(60), "\n";
file_put_contents('theta.html', $density->html());
$spec = $density->vegaLite(width: 480, height: 240);

theta: kernel density (bandwidth 0.02252)
  |               ********
  |             ***      ***
  |            **          **
  |           **            ***
2 +          **               **
  |         **                 ****
  |        **                     ***
  |      ***                        ****
  |     **                             *******
0 +******                                    ******************
  +----+--------------------------------+----------------------
       0                               0.5
   theta (y: density)

intervals: 50% inner, 90% outer, point = median
theta |-----------[=========o==========]--------------------
      +-----------------+--------------------------+--------
                       0.2                        0.4
       - outer, [=] inner, o = median

The figure functions follow bayesplot’s names and return a Figure. A figure holds the computed statistics in data, as documented on the Figure class, and renders them in several forms:

• ascii(width, height) returns plain ASCII text for a terminal, log, or text report. Echoing a figure prints this form with default sizes.
• vegaLite(width, height, maxRows) returns a Vega-Lite 5 spec as a PHP array with the data inlined, and json() returns the same spec as JSON that is safe to place in an HTML script element. Front ends render it with vega-embed or any other Vega-Lite runtime.
• html() returns a standalone page that loads Vega, Vega-Lite, and vega-embed from the jsDelivr CDN.
• svg() and png(scale: 2.0) render static images with vl-convert, a standalone binary that needs no Node or browser. Set VL_CONVERT to its path or put vl-convert on PATH.

The available figures are:

• mcmc_trace($fit, 'theta'): chains overlaid by iteration.
• mcmc_hist($fit, 'theta', bins: 30): histogram of all draws.
• mcmc_dens($fit, 'theta') and mcmc_dens_overlay($fit, 'theta'): Gaussian kernel density of all draws, or one curve per chain.
• mcmc_intervals($fit, ['mu', 'beta'], prob: 0.5, probOuter: 0.9, pointEst: 'median'): inner and outer intervals with a point estimate on a shared axis. Without a selection it plots every variable except lp__.
• mcmc_rank_hist($fit, 'theta', bins: 20): per-chain histograms of pooled ranks, with the count expected under uniform ranks marked.
• mcmc_scatter($fit, 'mu', 'sigma'): joint draws, with divergent transitions marked on MCMC fits.
• mcmc_acf($fit, 'theta', lags: 20): per-chain autocorrelation bars.
• pareto_k_plot($fit->loo()): Pareto k by observation, with the k threshold and k = 1 marked.

A plotted variable names one element, such as beta[2]. mcmc_intervals() also accepts base names, which select every element. The functions take a fit or a draws_array.

The bandwidth (R’s bw.nrd0), densities, quantiles, ranks, and autocorrelations are computed in PHP and checked against R and bayesplot. Vega-Lite specs carry these values and use no Vega-Lite density, binning, or quantile transforms, so every rendering shows the same numbers. The ASCII form rounds positions to character cells; use the figure’s data or the numeric methods, such as summary(), when exact values matter.

Trace and scatter figures inline every draw. For large fits, maxRows keeps every k-th iteration of a trace, or every k-th draw of a scatter plus all divergent draws, so that about that many rows remain. Per-chain figures (rank histograms and autocorrelation) are faceted by chain, and their sizes apply to each chain’s panel.