[Paper Review] SimSIMS: Simulation-based Supernova Ia Model Selection with thousands of latent variables

Konstantin Karchev, Roberto Trotta+1 more|arXiv (Cornell University)|Nov 27, 2023

Gamma-ray bursts and supernovae4 citations

TL;DR

This paper introduces SimSIMS, a simulation-based Bayesian model selection framework using neural networks to compare supernova Ia models with over 4,000 latent variables. It demonstrates Occam’s razor in action, favoring a single dust law and no magnitude step with posterior odds exceeding 100:1, while disfavoring split dust laws across host galaxy masses.

ABSTRACT

We present principled Bayesian model comparison through simulation-based neural classification applied to SN Ia analysis. We validate our approach on realistically simulated SN Ia light curve data, demonstrating its ability to recover posterior model probabilities while marginalizing over >4000 latent variables. The amortized nature of our technique allows us to explore the dependence of Bayes factors on the true parameters of simulated data, demonstrating Occam's razor for nested models. When applied to a sample of 86 low-redshift SNae Ia from the Carnegie Supernova Project, our method prefers a model with a single dust law and no magnitude step with host mass, disfavouring different dust laws for low- and high-mass hosts with odds in excess of 100:1.

Motivation & Objective

• To address the long-standing controversy over the existence of a magnitude step in Type Ia supernovae correlated with host galaxy mass.
• To perform Bayesian model comparison in the presence of >4,000 latent variables, including host mass, dust properties, and residual scatter.
• To overcome limitations of traditional likelihood-based methods in handling complex, high-dimensional hierarchical models with selection effects and non-linear dust laws.
• To validate the method on realistic simulated light curves and apply it to real low-redshift SN Ia data from the Carnegie Supernova Project.
• To demonstrate the scalability and principled nature of simulation-based inference for future large-scale cosmological analyses.

Proposed method

• The method employs neural simulation-based inference (SBI) with a normalizing flow-based neural network to approximate the posterior distribution over model parameters.
• A separate neural network is trained to classify models based on simulated data, enabling amortized computation of Bayes factors across multiple models.
• The approach marginalizes over all latent variables—including host stellar mass, dust law parameters (R_V), magnitude step, and residual scatter—without explicit likelihood evaluation.
• Model comparison is performed via posterior model probabilities derived from simulated data, with validation using known ground-truth parameters in synthetic datasets.
• The framework incorporates realistic physical effects such as non-linear dust laws, selection effects, and peculiar velocity uncertainties through a stochastic simulator.
• The method supports full Bayesian inference with guaranteed frequentist coverage and enables exploration of model dependence on true underlying parameters.

Experimental results

Research questions

• RQ1 Does a magnitude step in SN Ia brightness exist, correlated with host galaxy stellar mass?
• RQ2 Are distinct dust laws required for low- and high-mass host galaxies, or is a single global dust law sufficient?
• RQ3 How do model selection results depend on the prior volume and complexity, particularly in the context of Occam’s razor?
• RQ4 Can simulation-based inference reliably recover posterior model probabilities in high-dimensional models with >4,000 latent variables?
• RQ5 How do residual scatter and dust law variability affect the detection of a magnitude step?

Key findings

• The model with a single global dust law and no magnitude step has a posterior probability of 45%, significantly exceeding its prior of 16.6%.
• A split dust law for low- and high-mass hosts is disfavored with posterior odds exceeding 100:1, contrary to previous studies by Thorp & Mandel and Brout & Scolnic.
• The magnitude step is estimated at ΔM ≈ -0.05, with a 2σ significance, consistent with the TM22 analysis.
• Residual scatter σ_res is estimated at ≈0.2, higher than in TM22 (≈0.1), due to inclusion of unmodeled effects like peculiar velocities.
• Marginal posteriors for R_V and σ_R_V are consistent with TM22, and the split-dust model is disfavored primarily due to its larger prior volume.
• The method successfully demonstrates Occam’s razor, showing that simpler models are preferred when they explain the data adequately.