Module: aprender::bayesian
Public module of the aprender-core crate.
Source
crates/aprender-core/src/bayesian.rs or directory.
Example
use aprender::bayesian::{BetaBinomial, NormalInverseGamma, BayesianLinearRegression};
// See `cargo doc -p aprender-core --open` for full API reference.Module summary
aprender::bayesian exposes the closed-form conjugate-prior distributions
that make Bayesian updating tractable (Beta-Binomial, Dirichlet-Multinomial,
Gamma-Poisson, Normal-Inverse-Gamma) plus full Bayesian linear and logistic
regression. Conjugate priors give you posterior mean / mode / variance in
constant time after each observation — ideal for online experiment
analysis (A/B tests), bandits, and small-sample inference where you need
uncertainty estimates not just point predictions.
Key types
| Type | Description |
|---|---|
BetaBinomial | Beta prior over a binomial proportion. uniform(), jeffreys(), new(alpha, beta) constructors; update(successes, trials) for sequential inference. |
DirichletMultinomial | Dirichlet prior over multinomial probabilities. |
GammaPoisson | Gamma prior over a Poisson rate. |
NormalInverseGamma | NIG prior over unknown mean + variance. |
BayesianLinearRegression | Linear regression with full posterior over coefficients + noise. Exposes predict, log_likelihood, aic, bic. |
BayesianLogisticRegression | Laplace-approximated Bayesian logistic regression. |
Usage patterns
Pattern 1: Sequential A/B-test analysis with Beta-Binomial
use aprender::bayesian::BetaBinomial;
// Start from a Jeffreys prior, then ingest 7 successes out of 10 trials.
let mut posterior = BetaBinomial::jeffreys();
posterior.update(7, 10);
let mean = posterior.posterior_mean();
let var = posterior.posterior_variance();
println!("posterior mean = {:.3} variance = {:.4}", mean, var);
assert!(mean > 0.5);Pattern 2: Bayesian linear regression with predictive variance
use aprender::bayesian::BayesianLinearRegression;
use aprender::primitives::{Matrix, Vector};
let x = Matrix::from_vec(4, 1, vec![1.0, 2.0, 3.0, 4.0]).expect("4x1");
let y = Vector::from_slice(&[3.0, 5.0, 7.0, 9.0]);
let mut blr = BayesianLinearRegression::new(1);
blr.fit(&x, &y).expect("blr fit");
let coefs = blr.posterior_mean().expect("fitted");
let noise = blr.noise_variance().expect("fitted");
println!("posterior_mean = {:?} noise_var = {:?}", coefs, noise);
let x_test = Matrix::from_vec(1, 1, vec![5.0]).expect("1x1");
let preds = blr.predict(&x_test).expect("predict");
println!("y(5) ≈ {:.2}", preds[0]);See also
linear_model— frequentist alternatives (OLS / Ridge / Lasso)glm— generalized linear models for non-Gaussian responsesnaive_bayes(inclassification) — Bayes classifier variantmonte_carlo— when the posterior is not conjugate, fall through to MCMC
Full API
Run cargo doc -p aprender-core --open for the rendered rustdoc, or browse
docs.rs/aprender for the published version.