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Latent characterisation of the complete BATSE gamma ray bursts catalogue using Gaussian mixture of factor analysers and model-estimated overlap-based syncytial clustering

Fan Dai, Ranjan Maitra

TL;DR

The paper tackles the long-standing question of GRB subpopulations in the BATSE catalog by applying a two-tier statistical framework: a Gaussian mixture of factor analysers (MixFAD) to identify five ellipsoidal groups among 1150 thinned, complete GRBs with nine observed features, and model-estimated overlap-based syncing (MOBSynC) to merge these into higher-level composites. It demonstrates that the five simple groups merge into three and then two composite clusters, revealing a multi-layer GRB structure that can be interpreted in terms of latent factors and aligns with the Duration–Fluence–Spectrum scheme. The approach provides a coherent explanation for conflicting results in the literature (two, three, or five groups) by embedding a syncytial clustering perspective within a probabilistic, factor-analytic framework. The work yields compact, latent-factor descriptions of both simple and composite GRB groups, offering a nuanced, hierarchical view of GRB variability with potential applicability to other astrophysical datasets. It also identifies practical limitations and avenues for future extensions, such as incorporating measurement errors and missing data into MixFAD and extending factor flexibility across clusters.

Abstract

Characterising and distinguishing gamma-ray bursts (GRBs) has interested astronomers for many decades. While some authors have found two or three groups of GRBs by analyzing only a few parameters, recent work identified five ellipsoidally-shaped groups upon considering nine parameters $T_{50}, T_{90}, F_1, F_2, F_3, F_4, P_{64}, P_{256}, P_{1024}$. Yet others suggest sub-classes within the two or three groups found earlier. Using a mixture model of Gaussian factor analysers, we analysed 1150 GRBs, that had nine parameters observed, from the current Burst and Transient Source Experiment (BATSE) catalogue, and again established five ellipsoidal-shaped groups to describe the GRBs. These five groups are characterised in terms of their average duration, fluence and spectrum as shorter-faint-hard, long-intermediate-soft, long-intermediate-intermediate, long-bright-intermediate and short-faint-hard. The use of factor analysers in describing individual group densities allows for a more thorough group-wise characterisation of the parameters in terms of a few latent features. However, given the discrepancy with many other existing studies that advocated for two or three groups, we also performed model-estimated overlap-based syncytial clustering (MOBSynC) that successively merges poorer-separated groups. The five ellipsoidal groups merge into three and then into two groups, one with GRBs of low durations and the other having longer duration GRBs. These groups are also characterised in terms of a few latent factors made up of the nine parameters. Our analysis provides context for all three sets of results, and in doing so, details a multi-layered characterisation of the BATSE GRBs, while also explaining the structure in their variability.

Latent characterisation of the complete BATSE gamma ray bursts catalogue using Gaussian mixture of factor analysers and model-estimated overlap-based syncytial clustering

TL;DR

The paper tackles the long-standing question of GRB subpopulations in the BATSE catalog by applying a two-tier statistical framework: a Gaussian mixture of factor analysers (MixFAD) to identify five ellipsoidal groups among 1150 thinned, complete GRBs with nine observed features, and model-estimated overlap-based syncing (MOBSynC) to merge these into higher-level composites. It demonstrates that the five simple groups merge into three and then two composite clusters, revealing a multi-layer GRB structure that can be interpreted in terms of latent factors and aligns with the Duration–Fluence–Spectrum scheme. The approach provides a coherent explanation for conflicting results in the literature (two, three, or five groups) by embedding a syncytial clustering perspective within a probabilistic, factor-analytic framework. The work yields compact, latent-factor descriptions of both simple and composite GRB groups, offering a nuanced, hierarchical view of GRB variability with potential applicability to other astrophysical datasets. It also identifies practical limitations and avenues for future extensions, such as incorporating measurement errors and missing data into MixFAD and extending factor flexibility across clusters.

Abstract

Characterising and distinguishing gamma-ray bursts (GRBs) has interested astronomers for many decades. While some authors have found two or three groups of GRBs by analyzing only a few parameters, recent work identified five ellipsoidally-shaped groups upon considering nine parameters . Yet others suggest sub-classes within the two or three groups found earlier. Using a mixture model of Gaussian factor analysers, we analysed 1150 GRBs, that had nine parameters observed, from the current Burst and Transient Source Experiment (BATSE) catalogue, and again established five ellipsoidal-shaped groups to describe the GRBs. These five groups are characterised in terms of their average duration, fluence and spectrum as shorter-faint-hard, long-intermediate-soft, long-intermediate-intermediate, long-bright-intermediate and short-faint-hard. The use of factor analysers in describing individual group densities allows for a more thorough group-wise characterisation of the parameters in terms of a few latent features. However, given the discrepancy with many other existing studies that advocated for two or three groups, we also performed model-estimated overlap-based syncytial clustering (MOBSynC) that successively merges poorer-separated groups. The five ellipsoidal groups merge into three and then into two groups, one with GRBs of low durations and the other having longer duration GRBs. These groups are also characterised in terms of a few latent factors made up of the nine parameters. Our analysis provides context for all three sets of results, and in doing so, details a multi-layered characterisation of the BATSE GRBs, while also explaining the structure in their variability.
Paper Structure (17 sections, 20 equations, 6 figures, 8 tables)

This paper contains 17 sections, 20 equations, 6 figures, 8 tables.

Table of Contents

  1. Introduction
  2. Statistical Framework for Clustering
  3. Clustering with Gaussian Mixture of Factor Analysers
  4. Gaussian Mixture Model-based Clustering
  5. Gaussian Mixture of Factor Analysers MBC
  6. Choosing the number of mixture components and latent factors
  7. Model-estimated Overlap-Based Syncytial Clustering
  8. Overlap Measures between Simple Clusters
  9. Overlap Measures between Compound Clusters
  10. The MOBSynC Procedure
  11. An Illustrative Example
  12. Statistical Analysis of GRBs
  13. Simple ellipsoidal cluster analysis using MixFAD
  14. Identifying complex structure in the groups
  15. Additional interpretation of our results
  16. ...and 2 more sections

Figures (6)

  • Figure 1: Densities and scatter plots of the nine features (after $\log_{10}$ transformation) for the 1598 complete BATSE Catalog GRBs. Correlations between features are shown in the upper panel.
  • Figure 2: Violin plots of the relative errors (in $\log_{10}$ scale) of all nine parameters: (a) two flux arrival times (b) four time-integrated fluences, and (c) three peak fluxes, for the 1598 complete BATSE Catalog GRBs.
  • Figure 3: Simulated dataset: (a) 3D scatter plot showing the true clustering structure, with each different color representing ellipsoidally-shaped Gaussian clusters and the lighter and darker colors representing a complex-shaped "V" and a similar "U" cluster, (b) the estimated clusters from GMMBC that finds five ellipsoidally-shaped groups with (c) pairwise overlaps, and (d) the composite clusters from MOBSynC recolored to emphasize the composite and compound structure elicited by the algorithm.
  • Figure 4: BIC for each $K$ and $q$ upon fitting the Gaussian mixture of factor analysers with the 1150 thinned complete BATSE Catalog GRBs. The minimum BIC is attained at $(K,q) = (5,5)$.
  • Figure 5: The pairwise and generalised overlap measures between (a) the simple clusters at the end of the MixFAD algorithm, and (b) between the groups at the end of the first stage of merging.
  • ...and 1 more figures

Theorems & Definitions (3)

  • Remark 1
  • Remark 2
  • proof