Internship Objectives
The goal of this internship is to design and study a minimal, fully self-contained toy pipeline for CMB B-mode analysis, and to apply Simulation-Based Inference to infer key parameters such as:
- the tensor-to-scalar ratio r,
- the dust foreground amplitude Adust,
- and/or the noise amplitude σₙ.
The student will explore whether SBI can provide improved posterior estimation compared to standard Gaussian likelihood approaches, in a controlled and computationally light setting.
Work Plan
0. Implementation of the framework (Weeks 1-2)
- explore existing and open-access tools; assess their capabilities
- design/conception of the needed framework, in connection with FURAX
- simple validation cases, profiling, etc.
1. Forward simulation of polarized skies (Weeks 3 - 4)
- Generate low-resolution polarized CMB maps with varying r (e.g., nside = 16–32).
- Add a simple polarized dust component (PySM3 or analytic template).
- Include white and/or correlated noise.
- Extract summary statistics (pixel maps, or EE/BB pseudo-spectra).
2. Application of Simulation-Based Inference (Weeks 4 - 6)
- Implement SBI using libraries such as sbi, swyft, or JAX-based flows.
- Train neural posterior estimators for {r}, {r, A_dust}
- Assess convergence, degeneracies, and the ability of SBI to capture non-Gaussian structures.
3. Benchmark against classical methods (Weeks 6 - 8)
- Implement a standard Gaussian likelihood on maps or spectra.
- Compare posteriors from likelihood vs SBI: bias, variance, robustness to foreground uncertainty.?
4. Optional Extensions (Weeks 8 - 10)
Depending on progress:
- explore compressed summaries for SBI,
- infer a simple noise or systematic parameter (e.g. a 1/f knee),
- prototype a small JAX-based differentiable simulator.
Expected Outcomes
- A complete and transparent toy pipeline for B-mode analysis.
- Neural posterior estimators trained on simulated CMB data.
- A quantitative comparison between SBI and classical inference.
- A short scientific report, the oral presentation in front of the M2 jury, and reusable notebooks, contributing to ERC SciPol methodological developments.