Likelihood Functions

Overview

Functions of src/xi_protocol1b_bao_run.py that load the data and evaluate the posterior. Definition and interpretation: Likelihood Functions (concept page).

Data loaders

# src/xi_protocol1b_bao_run.py
def load_pantheon_data(filepath: Path, zcut: float = 0.01)
    -> (z, mu, mu_err, kept_idx, n_rows_total)
def load_pantheon_covariance(cov_filepath: Path, kept_idx: np.ndarray)
    -> (cov, cov_inv)
def load_desi_bao(mean_filepath: Path, cov_filepath: Path)
    -> (z_bao, types, values, cov, cov_inv)

Function	Raises
load_pantheon_data	FileNotFoundError if the file is missing; ValueError listing the columns if zHD, MU_SH0ES, MU_SH0ES_ERR_DIAG (or their SHOES spellings) are absent
load_pantheon_covariance	FileNotFoundError; ValueError if the entry count is not N²
load_desi_bao	FileNotFoundError; ValueError if no row can be read or the covariance shape does not match

z, mu and mu_err are already restricted to z > zcut; kept_idx indexes the original rows and must be passed to load_pantheon_covariance so that the matrix is cut consistently. See Covariance Handling.

log_prior

def log_prior(params: np.ndarray, model: str) -> float

Returns 0.0 inside the model's bounds and -inf outside (including for an unknown model name). Bounds: Prior Specification. For Ξosc: 0 < ε < 0.3.

χ² functions

def chi2_sn(params, model, z_sn, mu_sn, C_sn_inv, xi_helper=None) -> float
def chi2_bao(params, model, z_bao, types_bao, vals_bao, C_bao_inv, xi_helper=None) -> float
def chi2_combined(params, model, data: tuple, xi_helper=None) -> float

data is the tuple (z_sn, mu_sn, C_sn_inv, z_bao, types_bao, vals_bao, C_bao_inv). chi2_combined is chi2_sn + chi2_bao. All three return the quadratic form Δᵀ C⁻¹ Δ with the inverse covariance passed in.

log_probability

def log_probability(params, model, data, xi_helper=None) -> float

Returns log_prior − ½ chi2_combined, or -inf as soon as the prior is violated — without evaluating the χ². This is the function handed to emcee.EnsembleSampler.

Example

import numpy as np
from xi_protocol1b_bao_run import log_probability, XiOscillator   # src/ on sys.path

# data = (z_sn, mu_sn, C_sn_inv, z_bao, types_bao, vals_bao, C_bao_inv) from the loaders above
lp = log_probability(np.array([70.0, 0.3]), "LCDM", data)            # illustrative parameters

Notes

• Parameter vectors are ordered as in MODEL_LABELS.
• xi_helper is only used by "Xi_osc".
• Every call recomputes the distance grids; there is no caching.