MCMC sampling

Use liesel.goose to draw posterior samples. Choose a sampling method (a kernel) for each parameter block, then let Goose run the chains.

This complete example estimates a normal mean with a normal prior:

import jax.numpy as jnp
import tensorflow_probability.substrates.jax.distributions as tfd

import liesel.goose as gs
import liesel.model as lsl

mu = lsl.Var.new_param(
    0.0,
    dist=lsl.Dist(tfd.Normal, 0.0, 2.0),
    name="mu",
    inference=gs.MCMCSpec(gs.NUTSKernel, jitter_dist=tfd.Normal(0.0, 0.2)),
)
y = lsl.Var.new_obs(
    jnp.array([0.8, 1.3, 0.9, 1.6, 1.1]),
    dist=lsl.Dist(tfd.Normal, mu, 1.0),
    name="y",
)
model = lsl.Model(y)

results = gs.LieselMCMC(model).run_for_epochs(
    seed=2026,
    num_chains=4,
    adaptation=1000,
    posterior=1000,
    show_progress=False,
)

summary = gs.Summary(results)
samples = results.get_posterior_samples()

liesel.goose.engine - INFO - Initializing kernels...

liesel.goose.engine - INFO - Done

liesel.goose.engine - INFO - Finished warmup

summary.to_dataframe()[["mean", "sd", "ess_bulk", "rhat"]].round(3)

	mean	sd	ess_bulk	rhat
variable
mu	1.079	0.426	1678.736	1.003

The summary reports estimates and diagnostics; check both before using the draws. samples["mu"] has shape (4, 1000): chains first, then posterior draws. Adaptation tunes the sampler and is excluded from these draws.

Every parameter you intend to sample needs a kernel. The high-level helper reads MCMCSpec objects from the model; it does not assign a default kernel to parameters without one.

Start here

• Overview
• First posterior
• NUTS and Gibbs

Common tasks

• Choose kernels
• Choose initial values
• Configure sampling
• Check diagnostics
• Use posterior draws
• Compare predictions
• Use the engine
• Reproducibility
• Custom kernels

For exact arguments and defaults, see the MCMC.