cloelike: A Python Library for Cosmological Likelihood Inference in the Euclid Era

Technical Summary of cloelike: A Python Library for Cosmological Likelihood Inference in the Euclid Era

Problem Statement
The ESA Euclid mission aims to probe dark energy, dark matter, and primordial density perturbations through high-precision photometric and spectroscopic observations. Achieving these goals requires robust, validated, and reproducible likelihood frameworks for statistical inference. While the cosmological community possesses extensive inference tools (e.g., CosmoSIS, Cobaya), existing public likelihood implementations often suffer from two limitations: they are frequently probe-specific, or they lack the modularity and native data-format compatibility required for fully integrated, end-to-end Euclid analyses. There is a need for a unified, lightweight interface dedicated to computing the $\chi^2$ statistic that can seamlessly integrate with external Bayesian frameworks while adhering strictly to Euclid data standards.

Methodology and Software Design
cloelike is a Python package designed to address these limitations by providing a modular, composable library for Gaussian likelihood inference. Its architecture is built on a strict separation of concerns:

1. Core Functionality: The package focuses exclusively on evaluating the standard multivariate Gaussian log-likelihood:
   $$-2 \ln \mathcal{L} = (\mathbf{d} - \mathbf{t})^T \mathbf{C}^{-1} (\mathbf{d} - \mathbf{t}) + b$$
   where $\mathbf{d}$ is the data vector, $\mathbf{t}$ is the theoretical prediction, $\mathbf{C}$ is the covariance matrix, and $b$ is an additive bias. It does not perform parameter sampling or model management, delegating these tasks to external engines (e.g., Cobaya, CosmoSIS, Nautilus).

2. Modular Architecture:

   • Base Classes: For photometric probes, a shared base class handles data-vector ingestion, masking, scale cuts, covariance loading, precision-matrix handling, and consistency checks.
   • Mixins: Theoretical observable computations are delegated to independent, probe-specific mixins (e.g., harmonic-space angular power spectra, configuration-space correlation functions, COSEBIs). This design avoids code duplication and allows new observables to be added by implementing only the theoretical prediction module.
   • Protocol-Based Integration: cloelike interfaces directly with the cloelib theoretical prediction library using Python protocols. This ensures that likelihood definitions and theory computations remain decoupled, allowing cloelike to benefit immediately from updates in non-linear modeling (e.g., galaxy bias, redshift-space distortions) within cloelib.

3. Data Compatibility: The library operates on data vectors, covariance matrices, and theoretical predictions structured within the euclidlib data format. It supports:

   • Photometric Probes: Harmonic angular power spectra and real-space two-point correlation functions for Weak Lensing (WL), Photometric Galaxy Clustering (GCph), and Galaxy–Galaxy Lensing (GGL) in all joint combinations (3$\times$2pt, 2$\times$2pt).
   • Spectroscopic Probes: Full-shape power spectrum multipoles and Baryonic Acoustic Oscillations (BAO).

Key Contributions

• Unified Interface: cloelike provides a minimal, unified Python interface for computing $\chi^2$ statistics across all primary Euclid probes, supporting both photometric and spectroscopic data.
• Composability: The framework allows users to construct joint likelihoods (e.g., combining WL and GCph) by combining data containers, covariance representations, and observable providers without modifying the underlying infrastructure.
• Performance and Scalability: The implementation utilizes vectorized operations, caching of intermediate quantities (such as the inverse covariance matrix), and is compatible with parallel sampling codes to ensure efficiency in high-dimensional parameter spaces.
• Community Adoption: The software is actively used within the Euclid Consortium as the reference likelihood implementation, serving as a natural evolution of the former CLOE software.

Results and Usage
The paper demonstrates the library's utility through usage examples for two representative likelihoods:

1. Harmonic Photometric Likelihood: An example illustrates the initialization and evaluation of a log-likelihood for cosmic shear angular power spectra, detailing the construction of data dictionaries, scale cut settings, and the instantiation of the likelihood with specific cloelib background and perturbation classes.
2. Spectroscopic Full-Shape Likelihood: An example demonstrates the computation of a log-likelihood for spectroscopic galaxy clustering full-shape power spectra, including the handling of multipoles ($P_0, P_2, P_4$), fiducial cosmology extraction, unit rescaling, and the definition of nuisance parameters (e.g., galaxy bias, EFT parameters) across redshift bins.

Significance
The authors claim that cloelike lowers the barrier for the community to reproduce official Euclid results while enabling flexible exploration of new systematics and extended cosmological models. By acting as a dedicated, validated likelihood layer that complements existing end-to-end inference frameworks, it ensures interoperability without duplicating functionality. Its modular design facilitates the inclusion of novel observables (such as cross-correlations with the Cosmic Microwave Background) and supports the coherent multi-probe analyses necessary to extract the full scientific potential of Euclid survey data. The package is openly released under the MIT license to support community validation and reproducibility.