Beta–binomial coin toss
Bounded probability, beta prior, binomial likelihood, predictive RNG, and an exact beta(9,5) posterior.
Executable catalog · 0.8.0
Fifteen models that double as tests
Every example below is a named JUnit test. Together they exercise scripts, transforms, analytic gradients, NUTS, dense metrics, Metropolis, Gibbs, generated quantities, and difficult geometry. For a narrated first run, start with the fully worked CSV/JDM tutorial.
See BayesianShowcaseTest.javaConjugate and introductory
Start with models that have reference answers
Normal mean
Known observation variance, analytic factors, gradient checking, and a short NUTS run.
Normal location and scale
Vectorized data, a positive scale transform, exponential prior, and predictive normal draw.
Gamma–Poisson rate
Positive count rate, shape/rate gamma prior, Poisson likelihood, and count generation.
Bayesian A/B test
Two beta-binomial arms, two bounded parameters, gradient validation, and NUTS.
Regression and hierarchy
Write direct targets when the supported script subset is too small
Linear regression
Intercept and slope with Gaussian priors and likelihood.
Logistic regression
Stable log1p-exp likelihood and Bernoulli residual gradient.
Eight schools
Location, log scale, standardized effects, and a complete hierarchical gradient.
Cauchy location
A vectorized Cauchy likelihood limits the influence of one large outlier.
Geometry and multimodality
Exercise the warnings, not only the happy path
Neal’s funnel
Changing conditional scale tests analytic gradients and NUTS behavior.
Rosenbrock banana
A narrow curved ridge validates a nontrivial two-dimensional gradient.
Gaussian mixture
Stable log-sum-exp and random-walk Metropolis demonstrate a multimodal target.
Correlated Gaussian
A 0.9 correlation exercises dense mass-matrix adaptation.
Constraints and mixed state
Use the sampler that matches the state space
Dirichlet–multinomial
Stick-breaking transform, Jacobian, three-category likelihood, and gradient check.
Poisson change point
An exact discrete split update alternates with a Metropolis block for two log rates.
Reusable pattern
Each test follows the same compact discipline
DifferentiableLogDensity target = (state, gradient) -> {
// Return log density and replace every gradient coordinate.
};
assertTrue(Gradients.check(target, initial, 1e-5, 1e-5).passed());
ChainResult chain = new NoUTurnSampler().sample(
target, initial, options, new MersenneTwister(seed));
assertEquals(ChainResult.Status.SUCCESS, chain.status());Read the complete implementations in BayesianShowcaseTest.java. The shorter InferenceExamples.java is compiled against the packaged JAR by every check build.
Choose a next step
Turn examples into a reviewed analysis
Use the beginner tutorial for the end-to-end sequence, the diagnostics vignette for failure interpretation, and the script tutorial for text models.