bioniumx.detection.bayes_factor

bioniumx.detection.bayes_factor(evidence_m1: float, evidence_m2: float) → float[source]

Calculate the Bayes Factor (K) comparing two models.

The Bayes factor is the ratio of the marginal likelihoods (evidences) of two competing models. In atmospheric retrieval, M1 might be a model containing a specific molecule, and M2 is the model without it.

Parameters:

evidence_m1 (float) – Log-evidence (ln Z) for model 1.
evidence_m2 (float) – Log-evidence (ln Z) for model 2.

Returns:

K – The Bayes factor K = Z1 / Z2. Returns float(‘inf’) if numerical overflow.

Return type:

float

References

Trotta, R. (2008), Bayes in the sky: Bayesian inference and model selection in cosmology, Contemp. Phys., 49, 71-104.

Examples

>>> lnZ_with_h2o = -150.2
>>> lnZ_no_h2o = -155.4
>>> K = bayes_factor(lnZ_with_h2o, lnZ_no_h2o)
>>> print(f"Bayes factor for H2O: {K:.1f}")