NISMO

NISMO is a Python implementation of Morphing Importance Nested Sampling for Bayesian evidence estimation and weighted posterior inference. It uses a fixed, normalized importance distribution to define the nested-sampling target and supports rejection, random-walk, ensemble, and parallel replacement strategies.

NISMO is alpha research software. Validate evidence accuracy and sampling efficiency with repeated runs on your target problem. The fixed importance distribution must cover every region where the likelihood times prior is nonzero; missing support can bias the result. The adaptive-Morph proposal is explicitly heuristic and can also bias evidence estimates.

Installation

Install the standard user stack from PyPI:

python -m pip install "nismo[all]"

The base package requires only NumPy and SciPy. Optional extras are available individually:

• nismo[morph] adds MorphZ proposal fitting;
• nismo[plot] adds Matplotlib diagnostics;
• nismo[progress] adds the tqdm terminal/notebook display.

Until the first PyPI release is published, install the repository version with:

python -m pip install "nismo[all] @ git+https://github.com/nz-gravity/nismo.git@main"

Python 3.10 through 3.12 are tested.

Quick start

import numpy as np

from nismo import CallableModel, MorphProposal, NISMOSampler

LOG_2PI = np.log(2.0 * np.pi)


def log_likelihood(theta: np.ndarray) -> np.ndarray:
    return -0.5 * (theta[:, 0] ** 2 + LOG_2PI)


def log_prior(theta: np.ndarray) -> np.ndarray:
    return -0.5 * ((theta[:, 0] / 2.0) ** 2 + LOG_2PI) - np.log(2.0)


model = CallableModel(
    ndim=1,
    parameter_names=("x",),
    log_likelihood_fn=log_likelihood,
    log_prior_fn=log_prior,
)

# Representative posterior draws used only to fit the importance density.
training_rng = np.random.default_rng(7)
posterior_samples = training_rng.normal(scale=np.sqrt(0.8), size=(2_000, 1))
importance_morph = MorphProposal.fit(
    posterior_samples,
    param_names=model.parameter_names,
    groups=[],
)

result = NISMOSampler(
    model=model,
    importance_morph=importance_morph,
    n_live=200,
    rng=42,
).run(dlogz=1e-2, progress=True)

print(result.logz, result.logzerr, result.termination_reason)
weighted_samples = result.all_points
weights = result.posterior_weights
equal_weight_samples = result.resample_equal(rng=43, n_samples=10_000)

Both model functions receive batches with shape (n, ndim) and return one natural-log value per row. log_prior must be normalized and include every normalization constant. Posterior training samples fit the importance density; they are not reused as live points.

Documentation

• Documentation index
• Quick-start guide
• Configuration reference
• Results and diagnostics
• Complete public API

Runnable scripts and notebooks are under the examples/ directory.

Development

git clone https://github.com/nz-gravity/nismo.git
cd nismo
uv sync --extra dev
uv run ruff format --check .
uv run ruff check .
uv run mypy
uv run pytest -m "not slow"
uv build
uvx twine check dist/*

See the contribution guide and release guide.

License

NISMO is distributed under the BSD 3-Clause license.