Statistics Reference

Per-chain — SequenceStats

Returned by data.sequenceStats(variable, chain).

Field	Type	Description
mean	number	Arithmetic mean
stdev	number	Standard deviation
count	number	Number of draws
ess	number	ESS via FFT-based Geyer monotone estimator (single chain)
essPerDraw	number	ess / count
mcse	number	MCSE = stdev / √ess
skewness	number	Standardized third central moment
excessKurtosis	number	Standardized fourth central moment minus 3
autocorrelation	number[]	Autocorrelation values at lags 0, 1, 2, … (from FFT)

Note on standard deviation: The current implementation divides by n (population SD), not n-1 (sample SD). For typical MCMC chains (n ≥ 500) the difference is negligible. Skewness and kurtosis inherit this.

Per-variable — VariableStats

Returned by data.variableStats(variable). Aggregates across all chains.

Field	Type	Description
mean	number	Grand mean across all chains
stdev	number	SD of all draws pooled
count	number	Total draws across all chains
ess	number	Sum of single-chain ESS values
essPerDraw	number	ess / count
mcse	number	Multi-chain MCSE via bulk ESS
bulkEss	number	Rank-normalized bulk ESS (Vehtari 2021)
tailEss	number	Tail ESS for extremes (Vehtari 2021)
rhat	number | undefined	Rank-normalized R-hat = max(bulk, tail). undefined if < 2 chains
splitRhat	number | undefined	Simple split R-hat
geweke	{ z, pValue }	Geweke convergence test on pooled draws
skewness	number	Skewness of all draws pooled
excessKurtosis	number	Excess kurtosis of all draws pooled
quantiles	{ q5, q25, q50, q75, q95 }	Posterior quantiles
hdi90	[number, number]	90% Highest Density Interval
hdi90Width	number	Width of the 90% HDI

summary()

Returns VariableSummary[] — one row per variable, each row is { variable: string } & VariableStats.

const rows = data.summary();
// rows[0] = { variable: 'mu', mean: 1.23, rhat: 1.001, bulkEss: 4523, ... }

This is the data source for summaryTable() and the mcmc summary CLI command.