Choose initial values

Choose initial values#

Goose starts from the model’s current state. Choose values with finite log density on the correct support, then disperse the chains enough to reveal different behavior.

import jax.numpy as jnp
import numpy as np
import tensorflow_probability.substrates.jax.bijectors as tfb
import tensorflow_probability.substrates.jax.distributions as tfd

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

Prepare the example#

These examples require the regression model, including its transformation and inference specifications, from Sample your first posterior.

Check starting values#

For an existing Liesel model, call diagnose() to inspect its starting state.

Inspect values and log probabilities for NaN or infinity. For positive parameters sampled with NUTS, use a suitable transformation and initialize on its sampling scale. Finite density is necessary but does not ensure finite gradients or good mixing.

Disperse the chains#

For the regression model from Sample your first posterior:

joint = gs.MCMCSpec(
    gs.NUTSKernel,
    kernel_group="regression",
    jitter_dist=tfd.Normal(0.0, 0.2),
    jitter_method="additive",
)
model.vars["beta"].inference = joint
model.vars["log_sigma_sq"].inference = joint

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

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

liesel.goose.engine - INFO - Done

liesel.goose.engine - INFO - Finished warmup

Each chain receives its own perturbation. The scalar jitter distribution draws one perturbation per element of a vector parameter. A distribution with batch or event dimensions must match the parameter’s shape.

jitter_method

Starting value

Check

"additive"

Current value plus a draw.

The perturbation must respect support; a log parameter is often convenient.

"multiplicative"

Current value times a draw.

Use positive draws to keep a positive parameter positive.

"replacement"

The draw replaces the current value.

Choose a distribution with appropriate support and scale.

apply_jitter=True applies these configured distributions. It does not create random starts when jitter_dist is absent. Set apply_jitter=False to use the existing starts without their configured perturbations.

Start near a mode#

For a model prepared for unconstrained optimization, fit first and then update its state before building the sampler:

fit = opt.LieselOptim(
    model,
    optimizers="lbfgs",
    loss_monitor="train_full_data",
).fit()
model.state = model.update_state(fit.position_min_monitor, model.state)

liesel.optim.engine - INFO - Initializing optimization at epoch 0

Initializing:   0%|          | 0/1000 [00:00<?, ?it/s]

Train=1.448, Monitor=1.448:   1%|          | 10/1000 [00:01<02:47,  5.90it/s]

Train=1.448, Monitor=1.448:   2%|▏         | 19/1000 [00:01<01:41,  9.69it/s]

Fitting returns values separately; the assignment makes them the model’s starting state. The next LieselMCMC(model).run_for_epochs(...) call starts there and applies any configured jitter. See Optimization for fitting choices. A mode can be a useful start, but it does not establish exploration of the posterior or reveal other modes.

For individually supplied chain states, use set_initial_values() with multiple_chains=True. Each state leaf then needs a leading chain axis. Record starts and jitter settings along with the seed and environment.