Pulse Documentation

name: op-reg-bayes-linear
description: Bayesian linear regression with a conjugate Normal-Inverse-Gamma prior; emits posterior means, std errors, and credible intervals. Streams the same sufficient statistics as an OLS fit.
kind: operator
category: REG
operator: REG_BAYES_LINEAR
type: reference
applies_to: process, compose, predict
examples_tags: [regression, bayesian, streaming-friendly]

Regression operators emit coefficient + diagnostics; no Response.Components. Fit summaries ride Response.Regressions[i].

Use when

Fits a straight-line model of a numeric outcome under a prior, reporting each coefficient’s posterior mean and credible interval.

Questions it answers:

• Given the data and our prior belief, what range of values is plausible for the price coefficient?
• How do the coefficients shift when last year’s estimates are used as the prior?

Use something else:

• REG_GLM when the outcome is yes/no (0/1) or a count.

Params

Inputs

target / predictors — numeric analytics set: u4/u8/u16/u32/u64, f32/f64, decimal128, date, packed_bool, plus nullable variants. Nullable rows drop from n_obs.

Output

RegressionResult: Coefficients["(intercept)"] + per-predictor posterior-mean βs; StdErrors = the Student-t marginal’s SCALE (not the posterior SD, which is larger by √(ν/(ν−2))); CredibleIntervals[name] = [lower, upper] at credible_level; CILower / CIUpper the same t interval at conf_level (equal when unset), DF = 2a_n, ConfLevel; R2, AdjR2, ResidualStdErr, NObs; a robust covariance adds the Covariance echo. No PValues — Bayesian inference reports credibility, not tail probability. Streams the same Welford stats as OLS; one finalize-time Cholesky on Λ_n applies the conjugate posterior.

Reading the output

• coefficients.*: Posterior mean of the coefficient: the expected difference in the outcome between rows one unit apart on this predictor, holding the other predictors fixed, after combining the data with the prior.
• std_errors.*: Scale of the coefficient’s Student-t posterior: how uncertain the coefficient is given the data and the prior. With many rows it is close to the posterior standard deviation.
• conf_level: The coverage ci_lower and ci_upper were built at (the request’s conf_level, 0.95 by default).

Gotchas

• A probability weight in force (request, slot or Options.DefaultWeight) → PULSE_WEIGHT_UNSUPPORTED naming the kind; "weight": null runs it unweighted.
• penalty / alpha / l1_ratio / family / link rejected — other engines’ knobs.
• resample / selection → PROCESSING_CONFIG (not advertised) — credible intervals already convey uncertainty.
• prior_mu length ≠ predictors + 1 → PROCESSING_CONFIG.
• Robust covariance is a substitution, not a posterior: honest under heteroskedastic or dependent rows, but no longer the conjugate model’s probability statement. It forces the buffered path; < 2 clusters or a repeated order_by → PROCESSING_REGRESSION_VCOV_UNSUPPORTED.
• Vague-prior limit reproduces the OLS point estimate; intervals and ResidualStdErr run below OLS with few rows per predictor (σ² ≈ RSS/n, not RSS/(n−p−1)).
• R2 is on the posterior-mean fit, not averaged over posterior draws.

See

• pulse_examples_search tags=[bayesian]
• Skills: regression-modeling, op-reg-ols, op-reg-glm