[Paper Review] Robust sampling for weak lensing and clustering analyses with the Dark Energy Survey

P. Lemos, Weaverdyck, N.+69 more|arXiv (Cornell University)|Feb 16, 2022

Gaussian Processes and Bayesian Inference4 citations

TL;DR

This paper evaluates three Bayesian sampling algorithms—MultiNest, PolyChord, and Metropolis–Hastings—for weak lensing and clustering analyses in the Dark Energy Survey (DES) Y3 data. It finds that PolyChord provides the best balance of speed and robustness, yielding consistent Bayesian evidence and reliable credible intervals, and recommends specific settings for future cosmological analyses with DES Y3 data.

ABSTRACT

Recent cosmological analyses rely on the ability to accurately sample from high-dimensional posterior distributions. A variety of algorithms have been applied in the field, but justification of the particular sampler choice and settings is often lacking. Here we investigate three such samplers to motivate and validate the algorithm and settings used for the Dark Energy Survey (DES) analyses of the first 3 years (Y3) of data from combined measurements of weak lensing and galaxy clustering. We employ the full DES Year 1 likelihood alongside a much faster approximate likelihood, which enables us to assess the outcomes from each sampler choice and demonstrate the robustness of our full results. We find that the ellipsoidal nested sampling algorithm $ exttt{MultiNest}$ reports inconsistent estimates of the Bayesian evidence and somewhat narrower parameter credible intervals than the sliced nested sampling implemented in $ exttt{PolyChord}$. We compare the findings from $ exttt{MultiNest}$ and $ exttt{PolyChord}$ with parameter inference from the Metropolis-Hastings algorithm, finding good agreement. We determine that $ exttt{PolyChord}$ provides a good balance of speed and robustness, and recommend different settings for testing purposes and final chains for analyses with DES Y3 data. Our methodology can readily be reproduced to obtain suitable sampler settings for future surveys.

Motivation & Objective

• To assess the robustness and accuracy of different sampling algorithms in high-dimensional Bayesian inference for cosmological parameter estimation.
• To validate the choice of sampler and settings used in the DES Y3 combined weak lensing and clustering (3x2pt) analysis.
• To quantify the impact of sampler hyperparameters on posterior constraints and Bayesian evidence estimation.
• To provide a reproducible methodology for selecting optimal sampler settings in future cosmological surveys.
• To ensure that sampling-related uncertainties are negligible compared to statistical and systematic errors in cosmological constraints.

Proposed method

• Employs both the full DES Year 1 likelihood and a faster approximate likelihood to evaluate sampler performance efficiently.
• Compares three samplers: MultiNest (ellipsoidal nested sampling), PolyChord (sliced nested sampling), and Metropolis–Hastings (MCMC).
• Uses the Bayesian evidence and posterior credible intervals as key metrics to evaluate consistency and accuracy.
• Tests multiple hyperparameter configurations, including live point counts, tolerance levels, and repetition settings.
• Validates results against the Metropolis–Hastings algorithm as a reference for parameter inference.
• Applies the anesthetic and GetDist tools for posterior visualization and convergence diagnostics.

Experimental results

Research questions

• RQ1 How do different sampling algorithms (MultiNest, PolyChord, Metropolis–Hastings) compare in estimating Bayesian evidence and posterior credible intervals for DES Y3 data?
• RQ2 Does MultiNest produce consistent Bayesian evidence estimates across repeated runs, and how do its results compare to PolyChord?
• RQ3 To what extent do sampler hyperparameters (e.g., number of live points, tolerance) affect the accuracy and reliability of cosmological constraints?
• RQ4 Can the approximate likelihood reliably reproduce results from the full likelihood when testing sampler performance?
• RQ5 What are the optimal sampler settings for achieving robust and efficient inference in DES Y3 cosmological analyses?

Key findings

• MultiNest reports inconsistent Bayesian evidence estimates across repeated runs, indicating poor convergence and reliability.
• MultiNest produces somewhat narrower credible intervals for cosmological parameters than PolyChord, suggesting potential underestimation of uncertainties.
• PolyChord provides consistent Bayesian evidence and well-calibrated credible intervals, demonstrating superior robustness.
• The results from PolyChord and Metropolis–Hastings show good agreement, validating the reliability of PolyChord’s inference.
• PolyChord offers a favorable trade-off between computational speed and accuracy, making it suitable for large-scale cosmological analyses.
• The authors recommend specific settings for testing (e.g., higher tolerance, fewer live points) and final chains (e.g., lower tolerance, more live points) to balance efficiency and precision.