numpyro_schechter 1.0.0

Schechter galaxy luminosity distribution for NumPyro.

numpyro_schechter

Schechter galaxy luminosity distribution for NumPyro

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Overview

numpyro_schechter provides a NumPyro-compatible probability distribution for Bayesian inference with Schechter luminosity functions in absolute magnitude space.

Built for astronomers and statisticians, it includes a JAX-compatible, differentiable implementation of the upper incomplete gamma function, enabling stable and efficient modelling in probabilistic programming frameworks.

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Parameter Constraints

Due to the custom normalisation logic, some constraints apply:

• alpha must be real and non-integer.
• The valid range of alpha + 1 depends on alpha_domain_depth. By default, alpha_domain_depth=3, which supports the domain -3 < alpha + 1 < 3.
• To model more extreme values of alpha, increase the alpha_domain_depth parameter (see below).
• The list of valid depths is fixed and can be queried programmatically:

  from numpyro_schechter import SchechterMag
  SchechterMag.supported_depths()
  # -> [3, 4, 5, 6, 7, 8, 9, 10, 15, 20, 30]
  

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Installation

From PyPI:

pip install numpyro_schechter

From GitHub (latest development version):

pip install git+https://github.com/alserene/numpyro_schechter.git

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Usage

Here is a minimal example showing how to use the SchechterMag distribution:

import jax.numpy as jnp
import numpyro
import numpyro.distributions as dist
from numpyro_schechter.distribution import SchechterMag

# Simulated observed magnitudes
mag_obs = jnp.linspace(-24, -18, 100)

def model(mag_obs):
    # Priors
    alpha = numpyro.sample("alpha", dist.Uniform(-3.0, 1.0))
    M_star = numpyro.sample("M_star", dist.Uniform(-24.0, -20.0))
    logphi = numpyro.sample("logphi", dist.Normal(-3.0, 1.0))

    # Custom likelihood using the SchechterMag distribution
    schechter_dist = SchechterMag(alpha=alpha, M_star=M_star, logphi=logphi, mag_obs=mag_obs)
    
    # Use numpyro.factor to inject the log-likelihood
    log_likelihood = jnp.sum(schechter_dist.log_prob(mag_obs))
    numpyro.factor("likelihood", log_likelihood)

# You can now run inference with NumPyro's MCMC
# e.g., numpyro.infer.MCMC(...).run(rng_key, model, mag_obs=...)

# Note: Sampling is not implemented for SchechterMag; it is intended for use as a likelihood in inference.

For detailed usage and API documentation, please visit the Documentation.

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Development

If you want to contribute or develop locally:

git clone https://github.com/alserene/numpyro_schechter.git
cd numpyro_schechter
poetry install
poetry run pytest

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License

This project is licensed under the MIT License - see the LICENSE file.

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Contact

Created by Alice — [e-mail]

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Happy modelling!