API reference

Gaussian models

Here n is the number of observations and p is the number of predictors.

Function	Required inputs	Main controls	Result
fit_ridge	X (n × p), y (n)	draws, chains, prior_scale, random_state, feature_names	GaussianFit
fit_horseshoe	X, y	draws, burnin, chains, random_state, feature_names	GaussianFit
fit_spike_slab	X, y	draws, burnin, chains, random_state, feature_names	GaussianFit

Fitting requires at least two observations, finite numeric inputs and no constant predictor columns. Missing values are rejected. No intercept column should be added. GaussianFit.coefficient_draws has axes (chain, draw, predictor). intercept_draws and sigma2_draws have axes (chain, draw). extra stores prior scales and inclusion states; metadata records seeds and sampling controls.

fit.summary(interval=.95) returns a text table. fit.pooled_draws() explicitly combines chains for selection. fit.predict(X, interval=.95, include_noise=False) returns mean, lower, upper, interval and kind; intervals are pointwise posterior intervals. The point estimate is the posterior conditional mean; observation noise affects the intervals, not that point estimate. Preserve predictor order when predicting.

Posterior selection

Function	Required inputs	Main controls	Result
s2m	draws, thresholds	clustering, small_set, zero_draws, random_state, feature_names	TuningResult
two_means	draws	clustering, random_state, feature_names	SelectionResult
select	draws, count	feature_names	SelectionResult
spike_slab	draws	feature_names	SpikeSlabResult

A draw matrix has axes (draw, predictor). Exclude the intercept. Clustering requires at least two predictors; the other summaries allow one. Exact clustering is the default; clustering="kmeans" uses NumPy Lloyd iterations.

TuningResult contains thresholds, modal counts, per-draw counts, modal frequencies, selected sets and adjacent-set Jaccard similarities. select(i) uses the threshold at zero-based position i. SelectionResult reports selected indices, names, median absolute coefficients and per-draw counts where estimated.

SpikeSlabResult contains inclusion_probability, mpm, hppm, visited_models, model_counts and hppm_ties. Zero means an exact spike; no numerical tolerance converts continuous coefficients to exclusions. Each result has summary().

Sparse coefficients

Function	Required inputs	Controls	Result
savs	X, beta	feature_names	SparseResult
dss	X, beta, penalty	tol, max_iter, feature_names	SparseResult

X must have one nonzero-norm column per beta entry. No centering is added. The result contains coefficients, selected, converged, iterations, objective, diagnostics and metadata. SAVS does not optimize a DSS objective; its objective field is unavailable (NaN). predict(X, intercept=0) returns X times the sparse coefficients plus the supplied intercept. summary() returns a text summary.

Diagnostics and plotting

diagnostics(fit) includes beta, intercept and sigma². For external arrays, use diagnostics(draws, feature_names=...) with explicit (chain, draw, predictor) axes and at least four retained draws. Results contain rank R-hat, bulk/tail ESS, mean MCSE, flags and backend, plus summary(). ESS is effective sample size; MCSE estimates the numerical error of a sampled posterior mean.

Plot	Input	Other controls
plot_tuning	TuningResult	ax
plot_coefficients	GaussianFit	interval, selected, ax
plot_inclusion	SpikeSlabResult	ax
plot_trace	fit or chain array	variable, ax
plot_autocorrelation	fit or chain array	variable, max_lag, ax

All plots return axes. Variable and selected indices are zero-based. Coefficient plots show posterior means and equal-tail intervals, not selection-error rates.