petitRADTRANS.retrieval.log_likelihood

Classes

LogLikelihood

Functions

get_bic(→ float)	Calculate the Bayesian Information Criterion for a fitted model.
get_aic(→ float)	Calculate the Akaike Information Criterion for a fitted model.
get_bpics(→ float)	Calculate the simplified Bayesian Predictive Information Criterion.

Module Contents

petitRADTRANS.retrieval.log_likelihood.get_bic(max_logl: float, n_data: int, n_params: int) → float

Calculate the Bayesian Information Criterion for a fitted model.

References:

Schwartz (1978), DOI 10.1214/aos/1176344136. Thorngren et al. (2025), DOI 10.3847/1538-4365/ae0e71.

petitRADTRANS.retrieval.log_likelihood.get_aic(max_logl: float, n_params: int) → float

Calculate the Akaike Information Criterion for a fitted model.

References:

Akaike (1974), DOI 10.1109/TAC.1974.1100705. Thorngren et al. (2025), DOI 10.3847/1538-4365/ae0e71.

petitRADTRANS.retrieval.log_likelihood.get_bpics(logl_samples: jax.typing.ArrayLike, n_params: int, log_weights: jax.typing.ArrayLike = None) → float

Calculate the simplified Bayesian Predictive Information Criterion.

References:

Ando (2011), DOI 10.1080/01966324.2011.10737798. Thorngren et al. (2025), DOI 10.3847/1538-4365/ae0e71.

class petitRADTRANS.retrieval.log_likelihood.LogLikelihood(model_spectrum: jax.typing.ArrayLike, data_spectrum: jax.typing.ArrayLike, data_uncertainties: jax.typing.ArrayLike = None, data_covariance: jax.typing.ArrayLike = None, covariance_cholesky_factor: jax.typing.ArrayLike = None, log_likelihood_normalization: jax.typing.ArrayLike = None, n_free_parameters: int = 0)

model_spectrum

data_spectrum

n_data_points

n_free_parameters = 0

cholesky_factor = None

log_det_covariance = None

get_chi_squared() → float

_calculate_chi_squared_covariance()

_calculate_chi_squared_uncertainties()

calculate_log_likelihood() → float

get_reduced_chi_squared() → float

Calculates the reduced chi-squared value.

Returns:

The reduced chi-squared value. Returns jnp.nan if degrees of freedom is <= 0.

get_noise_normalization_constant() → float

Returns the noise-related normalization constant of the log-likelihood. This is -0.5 * (N*log(2pi) + log(det(Cov))) or -0.5 * sum(log(2pi*sigma_i^2)). This term does not depend on the model-data residuals.

Returns:

The pre-computed noise normalization constant.

log_likelihood(beta=None, beta_mode='multiply')

static _log_likelihood(model, data, uncertainties, beta=None, beta_mode='multiply')

Calculate the log-likelihood between the model and the data.

The spectrum model must be on the same wavelength grid than the data.

From Gibson et al. 2020 (https://doi.org/10.1093/mnras/staa228). Constant terms are dropped and constant coefficients are set to 1. The ‘add’ beta mode comes from Line et al. 2015 (DOI 10.1088/0004-637X/807/2/183).

Set:

chi2(A, B) = sum(((f_i - A * m_i) / (B * sig_i)) ** 2), implicit sum on i

with f_i the data, m_i the model, and sig_i the uncertainty; where “i” denotes wavelength/time variation. Starting from (implicit product on i):

L = prod(1 / sqrt(2 * pi * B * sig_i ** 2) * exp(-1/2 * sum(((f_i - A * m_i) / (B * sig_i)) ** 2))), => L = prod( 1 / sqrt(2 * pi * B * sig_i ** 2) * exp(-1/2 * chi2(A, B)) ), => ln(L) = -N/2 * ln(2 * pi) - N * ln(B) - sum(ln(sig_i)) - 1/2 * chi2(A, B).

Dropping constant terms:

ln(L)^* = - N * ln(B) - 1/2 * chi2(A, B).

B can be automatically optimised by nulling the ln(L) partial derivative with respect to B. Using the best estimator of B instead of the true value:

d_ln(L) / d_B = - N / B + 1 / B ** 3 * chi2(A, B=1) = 0, => B = sqrt( 1/N * chi2(A, B=1)).

Replacing:

ln(L)^**= - N * ln(B) - 1/2 * chi2(A, B),

= - N * ln(sqrt(1/N * chi2(A, B=1))) - 1/2 * sum(((f_i - A * m_i) / (B * sig_i)) ** 2), = - N/2 * ln(1/N * chi2(A, B=1)) - 1/2 / B ** 2 * sum(((f_i - A * m_i) / sig_i) ** 2), B cst with i = - N/2 * ln(1/N * chi2(A, B=1)) - 1/2 * N / chi2(A, B=1) * chi2(A, B=1), = - N/2 * ln(1/N * chi2(A, B=1)) - N/2.

Dropping constant terms:

ln(L)^*** = - N/2 * ln(1/N * chi2(A, B=1)).

Args:

model: numpy.ndarray

The model flux in the same units as the data.

data: numpy.ndarray

The data.

uncertainties: numpy.ndarray

The uncertainties on the data.

beta: float, optional

Noise scaling coefficient. If None, the noise scaling is “automatically optimised”.

beta_mode: string, optional

Returns:

logLfloat

The log likelihood of the model given the data.

static log_likelihood2chi2(log_likelihood: float) → float