[Paper Review] Machine Learning Model of the Swift/BAT Trigger Algorithm for Long GRB Population Studies

P. B. Graff, A. Y. Lien+2 more|arXiv (Cornell University)|Sep 3, 2015

Gamma-ray bursts and supernovae47 references3 citations

TL;DR

This paper develops a machine learning model to accurately emulate the Swift/BAT trigger algorithm for long gamma-ray bursts (GRBs), significantly improving detection efficiency modeling over traditional flux-based thresholds. Using simulated GRB data, random forest and AdaBoost models achieve >97% accuracy, enabling fast, fully Bayesian inference of the intrinsic GRB rate distribution, yielding a local rate density of $ n_0 \sim 0.48^{+0.41}_{-0.23} \, \text{Gpc}^{-3}\text{yr}^{-1} $ with a break redshift at $ z_1 \sim 6.8^{+2.8}_{-3.2} $.

ABSTRACT

To draw inferences about gamma-ray burst (GRB) source populations based on Swift observations, it is essential to understand the detection efficiency of the Swift burst alert telescope (BAT). This study considers the problem of modeling the Swift/BAT triggering algorithm for long GRBs, a computationally expensive procedure, and models it using machine learning algorithms. A large sample of simulated GRBs from Lien 2014 is used to train various models: random forests, boosted decision trees (with AdaBoost), support vector machines, and artificial neural networks. The best models have accuracies of $\gtrsim97\%$ ($\lesssim 3\%$ error), which is a significant improvement on a cut in GRB flux which has an accuracy of $89.6\%$ ($10.4\%$ error). These models are then used to measure the detection efficiency of Swift as a function of redshift $z$, which is used to perform Bayesian parameter estimation on the GRB rate distribution. We find a local GRB rate density of $n_0 \sim 0.48^{+0.41}_{-0.23} \ { m Gpc}^{-3} { m yr}^{-1}$ with power-law indices of $n_1 \sim 1.7^{+0.6}_{-0.5}$ and $n_2 \sim -5.9^{+5.7}_{-0.1}$ for GRBs above and below a break point of $z_1 \sim 6.8^{+2.8}_{-3.2}$. This methodology is able to improve upon earlier studies by more accurately modeling Swift detection and using this for fully Bayesian model fitting. The code used in this is analysis is publicly available online (https://github.com/PBGraff/SwiftGRB_PEanalysis).

Motivation & Objective

• Address the challenge of accurately modeling Swift/BAT's complex, multi-criteria triggering algorithm for long GRBs, which introduces significant selection biases in population studies.
• Overcome limitations of flux-based detection thresholds, which yield only 89.6% accuracy and fail to capture full instrumental selection effects.
• Develop a fast, reliable surrogate model of the Swift/BAT trigger using machine learning to accelerate Bayesian parameter estimation for GRB population models.
• Enable fully Bayesian inference on the intrinsic GRB rate distribution by incorporating accurate, empirical detection efficiency as a function of redshift.
• Provide a publicly available, extensible framework for future GRB population studies, including luminosity function fitting and model comparison.

Proposed method

• Train multiple machine learning algorithms—random forests, AdaBoost, support vector machines, and artificial neural networks—on a large sample of simulated long GRBs from Lien et al. (2014).
• Use the simulated GRBs as training data, where each instance includes GRB parameters (luminosity, redshift, duration, etc.) and the corresponding trigger outcome from the Swift/BAT pipeline.
• Optimize and validate models using cross-validation and performance metrics such as accuracy and area under the ROC curve.
• Construct an empirical detection efficiency function $ F_{\text{det}}(z) $ by applying the best-performing ML model to a grid of redshifts and fixed luminosity, accounting for all trigger criteria.
• Perform Bayesian parameter estimation using the ML-derived detection efficiency as a likelihood component, fitting a double-broken power-law model to both simulated and real redshift data.
• Use Markov Chain Monte Carlo (MCMC) sampling to explore the full posterior distribution, quantifying uncertainties and parameter degeneracies.

Experimental results

Research questions

• RQ1 What is the accuracy of machine learning models in emulating the full Swift/BAT trigger algorithm for long GRBs compared to simple flux thresholds?
• RQ2 How do different machine learning algorithms (random forest, AdaBoost, SVM, neural networks) compare in modeling the complex, multi-parameter trigger decision process?
• RQ3 What is the resulting detection efficiency of Swift as a function of redshift when using the best-performing ML model?
• RQ4 How does the use of ML-based detection efficiency improve Bayesian inference of the intrinsic GRB rate distribution compared to previous methods?
• RQ5 What are the posterior constraints on the local GRB rate density and power-law indices of the redshift distribution when using a fully Bayesian framework with ML-empirical likelihoods?

Key findings

• The random forest and AdaBoost models achieve the highest accuracy, exceeding 97.5%, significantly outperforming a simple flux threshold, which has only 89.6% accuracy.
• The support vector machine and neural network models achieve 94.7% and 96.9% accuracy, respectively, demonstrating strong performance but slightly below the top two models.
• The ML-based detection efficiency model enables fast, accurate likelihood evaluation, allowing full exploration of the parameter space with MCMC sampling.
• Using the ML-derived detection efficiency, the study finds a local GRB rate density of $ n_0 \sim 0.48^{+0.41}_{-0.23} \, \text{Gpc}^{-3}\text{yr}^{-1} $, with a break redshift at $ z_1 \sim 6.8^{+2.8}_{-3.2} $.
• The power-law indices for the GRB rate distribution are estimated as $ n_1 \sim 1.7^{+0.6}_{-0.5} $ (for $ z < z_1 $) and $ n_2 \sim -5.9^{+5.7}_{-0.1} $ (for $ z > z_1 $), consistent with previous studies.
• The framework is computationally efficient after training and is publicly available, enabling future extensions to include luminosity functions, multiple break points, and selection bias modeling.