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Overinflation and overconcentration: why Cauchy perturbation kernels are the right choice for ABC-SMC

Approximate Bayesian computation sequential Monte Carlo (ABC-SMC) propagates its particles with a perturbation kernel, and with the standard Normal kernel it degrades sharply as t

GIST

Approximate Bayesian computation sequential Monte Carlo (ABC-SMC) propagates its particles with a perturbation kernel, and with the standard Normal kernel it degrades sharply as the parameter dimension grows, a failure usually attributed to dimension itself. We show instead that it is governed by the quality of the summary statistics, with dimension entering only through a separate and milder mechanism, and that the two must act together for the Normal kernel to break. The first ingredient is covariance overinflation: the kernel covariance, estimated from the particle cloud, overshoots the true posterior covariance by a factor set by information loss in the summary statistics. We derive this overscaling factor in closed form for a Gaussian model with sufficient statistics and show that it stays modest at any dimension, shrinking toward its baseline value as the tolerance tightens; the extreme values seen in practice (of order 103) are a signature of insufficient summaries, not of dimension. The second ingredient is perturbation overconcentration: the normalised Normal step size concentrates around one as the dimension grows, so every proposal overshoots by the same factor.

Clinical Editorial

bioRxiv (Biomedical Preprints) published a clinical update in Research Highlights on 09 Jul 2026. The item focuses on Overinflation and overconcentration: why Cauchy perturbation kernels are the right choice for ABC-SMC. Review the original article for the full source wording and details.

Original source: https://www.biorxiv.org/content/10.64898/2026.06.24.734205v1?rss=1