API guide

Fit a model

Input	Function	Parameter being estimated
Effect estimates and standard errors	fit	Scalar effects under Gaussian or Student-t summary likelihoods
Counts and exposure times	fit_poisson	Nonnegative Poisson rates
Successes and trial counts	fit_binomial	Binomial probabilities
Effect matrices and error covariances	fit_multivariate	Effect vectors across conditions
Continuous outcomes and predictor matrix	fit_regression	Regression coefficients and predicted means
Binary/binomial outcomes and predictors	fit_logistic_regression	Log-odds coefficients and fitted probabilities
Counts, exposures and predictors	fit_poisson_regression	Log-rate coefficients and fitted counts
Continuous outcomes, predictors and groups	fit_mixed_regression	Fixed coefficients and random intercepts

In fit, family selects the prior: normal, uniform or halfuniform. A finite df selects a Student-t likelihood; its input standard-error value is the distribution's scale, not its standard deviation. Gaussian inputs use the usual standard error. null_weight=1 fits mixture weights by maximum likelihood; larger values add a penalty favouring the point-null component.

normal_mixture and uniform_mixture construct explicit scalar priors. Pass one through fit(..., prior=prior, fix_prior=True) to evaluate a fixed prior without estimating new weights. Summary-input results provide shrink to evaluate new observations with the fitted prior, without estimating new weights. Student-t results require the new observations' df. For count results, shrink(observations, auxiliary) takes exposure times or trial counts as its second argument.

When observations are counts, shrinkage must respect the parameter range. Poisson rates are nonnegative and binomial probabilities lie between zero and one. The Poisson and binomial methods therefore use Gamma and Beta mixtures with a specified common mode. Their parameter and null scales differ from scalar signed effects. These are conjugate-mixture extensions, not matched R ashr likelihoods.

When effects are measured across conditions, their relationships can inform shrinkage. Multivariate fitting uses supplied positive-semidefinite covariance patterns and positive-definite observation-error covariances; patterns and residual correlations are not learned from the effects.

For regression inputs, see the regression guide. Its coefficient distributions use a variational approximation; prediction returns outcome means.

Inspect posterior results

All results provide posterior_mean, posterior_sd, summary, cdf, quantile, interval and sample. summary returns reporting columns. Scalar, multivariate and regression results also have format_summary for compact text. sample draws latent parameters, not future observed data.

interval(level=.95) returns equal-tailed posterior credible intervals. They condition on the fitted mixture weights and selected component grid. lfdr is posterior point-null probability. lfsr is the smaller posterior probability of a nonpositive or nonnegative effect, including a zero atom in both error events. For count models, the directions are relative to the specified null rate or probability. qvalue and svalue average local null and sign-error probabilities at their respective cutoffs. They are posterior summaries, not automatic frequentist error-control guarantees. If the prior has no atom at the reported parameter's null value, lfdr and qvalue are zero by construction. This is a prior choice, not evidence against the null. In a multivariate model, a coordinate can retain an atom even without a whole-vector null component.

Multivariate results also provide posterior covariance matrices and the probability that the whole effect vector is zero. A coordinate can have a zero atom even when another coordinate does not. Marginal and whole-vector null probabilities therefore have different meanings.

Tables and saved results

Named-column adapters are fit_frame, fit_poisson_frame, fit_binomial_frame, fit_multivariate_frame and the regression _frame adapters. They accept pandas frames or mappings of columns. Scalar missing values are rejected by default; missing="drop" explicitly removes incomplete rows and retains their indices. Other fitting methods require complete data.

to_records returns plain rows; write_csv exports summaries. save_result and load_result use versioned JSON without pickle or code execution. Summary-input results reconstruct their posterior calculations; regression results restore their saved factors. Neither operation estimates new mixture weights. Saved results retain input estimates or counts. Regression JSON also retains training outcomes, directly or through fitted values and residuals; it is not an anonymized summary. result.to_dataframe() requires the table extra.

Plots

For summary-input fits, plot_shrinkage, plot_intervals, plot_prior and plot_diagnostics return Matplotlib axes. They do not call show or save files. For multivariate results, condition selects the column to display. Prior density plots keep point-null probability separate from continuous density. Regression has plot_coefficients and plot_residuals; plot_diagnostics displays the variational objective. Random-intercept fits also have plot_random_effects.