End-to-End Pipeline for CMB Polarization Analysis: From Time-Ordered Data to Cosmology, with a View Toward Simulation-Based Inference

Scientific Context & Motivation:
The SciPol project has laid the groundwork for a new generation of CMB polarization data analysis, with key contributions to:
 

• Accurate modeling of instrumental and astrophysical systematics (e.g. HWP modulation, polarized foregrounds, correlated noise),
• Development of scalable analysis pipelines based on JAX (e.g. FURAX, MegaTop),
• Explorations of conditional likelihoods and Gibbs sampling strategies for noise, sky and foreground modeling.

Despite these advances, much of the CMB analysis pipeline still relies on step-wise approximations and fixed intermediate quantities (e.g. maximum-likelihood maps, fixed foreground residuals), which can limit robustness and propagate biases.
The central objective of this PhD is to streamline and unify the end-to-end analysis pipeline from time-ordered data (TOD) to cosmological spectra, leveraging the tools developed within SciPol (e.g. FURAX, MegaTop) to ensure accurate propagation of instrument, noise, and component modeling across all stages of the analysis.
As a forward-looking extension, the project may explore Simulation-Based Inference (SBI) methods, which offer an alternative paradigm: instead of breaking the pipeline into decoupled steps, one can define a global probabilistic model and perform likelihood-free inference directly on cosmological and nuisance parameters using end-to-end forward simulations and neural posterior estimators.

Objectives of the PhD:
The first goal of the PhD is to consolidate and validate a realistic TOD-to-spectra analysis chain that incorporates filtering effects, correlated noise, beam mismatch, and component separation.
The project may then evolve toward the development and evaluation of a new, simulation-based inference framework for CMB polarization experiments, able to incorporate complex systematics and uncertain components at each stage of the pipeline:

1. Map-making layer: replace traditional GLS map-making with SBI approaches that marginalize over instrument noise, HWP modulation patterns, and pointing uncertainties;
2. Component separation layer: perform joint inference over cosmological signals and foreground parameters using SBI trained on forward-simulated skies (e.g. with PySM);
3. Cosmological inference layer: propagate all uncertainties (from maps, beams, noise, components) into the inference of cosmological parameters, especially tensor-to-scalar ratio r and birefringence angle.

This work would leverage the FURAX framework for end-to-end simulations and differentiable modeling, and target realistic SO and LiteBIRD-like configurations.

Tasks and Timeline (indicative):
Year 1:
Familiarize with the FURAX pipeline, SBI methods (SNPE, NPE, NRE, etc.), and CMB experimental models;
Define benchmark problems (e.g. polarized map-making with filtering, simplified comp-sep models);
Build proof-of-concept SBI setups (e.g. JAX-powered simulators + sbi or swyft library).
Year 2:
Scale up to more realistic pipelines (e.g. MegaTop for component separation);
Integrate SBI with full parameter space including spectral indices, beams, and correlated noise models;
Explore amortized vs local inference, diagnostics, coverage, and efficiency.
Year 3:
Apply framework to simulated data from SO or LiteBIRD-like configurations;
Compare performance with classical likelihood-based methods (e.g. Gibbs, MCMC on maps or spectra);
Explore extensions: Bayesian decision-making, active learning, or simulation-efficient strategies.

Expected Outcomes:
A novel framework for robust cosmological inference using simulation-based methods;
Demonstration of SBI for global CMB analysis in the presence of complex systematics;
Software and tools integrated with FURAX and reusable by the CMB community;
Applications to real or realistic data (e.g. SO small aperture telescope simulations, LiteBIRD sky maps).

Supervision & Collaborations:
Supervision: Josquin Errard and Radek Stompor
Collaborations: SciPol team (e.g. Wassim Kabalan, Pierre  Chanial, Wuhyun Sohn, Artem Basyrov, Benjamin Beringue), developers of FURAX, LiteBIRD and SO France teams
Possible joint developments with ML experts and external SBI researchers (e.g. from the CMB inference group at Flatiron, Cambridge/ETH SBI developers, Adri Duivenvoorden @ MPA)

Required Skills:
Strong background in cosmology, statistics and inference;
Experience or motivation to work with JAX, large-scale simulations, and probabilistic modeling;
Interest in methodological innovation and software development.