Highlights

• Log-domain P-spline models for positive PSDs.

• Multivariate Wishart likelihoods for spectral matrices.

• VI warm starts and factorised multivariate NUTS.

• Optional frequency-domain coarse graining.

• Scalar time-varying fits from WDM and moving-periodogram powers.

• Posterior PSD quantiles, coherence summaries, and diagnostic plots.

Install

For development, use the repository virtual environment:

source .venv/bin/activate
python -m pip install -e '.[dev]'

For package use:

python -m pip install LogPSplinePSD

Five-Minute Example

from log_psplines import StationaryConfig, fit
from log_psplines.example_datasets import VARMAData

data = VARMAData.ar(order=4, n_samples=8192, fs=64.0, seed=7)

result = fit(
    data.ts,
    StationaryConfig(
        n_knots=16,
        knot_kwargs={"method": "density"},
        vi_steps=200,
        n_warmup=100,
        n_samples=200,
        rng_key=7,
        true_psd=data.get_true_psd(),
    ),
)

frequency = result.frequency
psd_draws = result.psd

Next Steps

• Follow the univariate example.

• Explore the multivariate example.

• Try the time-varying example.

• Read the spectral conventions.

Architecture

See the development notes for the shared scalar/matrix model and time-frequency evaluation. Scalar time-varying power inference is available through fit(). Multivariate time-varying inference is not yet implemented.

Documentation

Build the docs locally with:

source .venv/bin/activate
.venv/bin/jupyter-book build docs

The public docs focus on package usage, configuration, outputs, API reference, and implementation notes. Domain-specific examples are intentionally kept out of the main docs for now and can be added later as separate studies.

References

Eilers, P. H. C., & Marx, B. D. (1996). Flexible smoothing with B-splines and penalties. Statistical Science, 11(2), 89-121.

Maturana-Russel, J., & Meyer, R. (2021). P-spline spectral density estimation with a discrete penalty. arXiv:1905.01832.

Vajpeyi, A., Meyer, R., Maturana-Russel, P., & Liu, J. (2026). Multivariate Bayesian P-spline estimation of spectral density matrices, with application to LISA TDI noise. arXiv:2607.04833. DOI:10.48550/arXiv.2607.04833.