What is it about?
Computational chemistry has many algorithms for finding transition states, but comparing their performance is harder than it looks. The usual approach -- run each method on a few test cases and report the average -- ignores the large variability between problems and gives no indication of how confident we should be in the ranking. We applied Bayesian hierarchical models to this benchmarking problem. The statistical model treats each test case as drawn from a population, estimates both the average performance and its spread, and produces full posterior distributions over rankings. This means we can say not just "method A is faster on average" but "method A is faster with 94% probability, and the expected difference is X minutes." We applied this framework to rank saddle point search algorithms on a set of molecular reactions, using metrics like wall time, number of force evaluations, and success rate.
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Why is it important?
Algorithm benchmarking in computational chemistry typically relies on point estimates (means, medians) without uncertainty quantification. This makes it hard to tell whether observed differences are real or just noise from a small test set. Bayesian hierarchical models address this directly. The posterior distributions account for problem-to-problem variability, finite sample size, and correlations between metrics. Performance profiles, widely used in optimization, complement the statistical analysis by showing cumulative solve rates as a function of computational budget. The framework applies to any algorithm comparison problem where test cases vary in difficulty. We provide the code and data for others to apply the same analysis to their own benchmarks.
Perspectives
This work grew from a practical need: I was comparing saddle point search methods for my thesis and found that the standard way of reporting results -- tables of means -- did not capture what I was seeing in the data. Some methods were fast on easy problems but failed on hard ones. Averages hid this. Bayesian hierarchical models turned out to be the right tool. They handle the nested structure (methods tested on problems) naturally and propagate uncertainty through to the final ranking. The brms package in R made the modeling accessible. The paper serves both as a methods contribution and as a benchmark for the GP-accelerated saddle search work in our other publications.
Rohit Goswami
University of Iceland
Read the Original
This page is a summary of: Bayesian hierarchical models for quantitative estimates for performance metrics applied to saddle search algorithms, AIP Advances, August 2025, American Institute of Physics,
DOI: 10.1063/5.0283639.
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