Constrained surrogates for arbitrary families of continuous probability distributions
Abstract
Empirical regularities described by parametrized families of probability distributions can shape how complex systems are interpreted and explained. A recurring problem is to determine the extent to which these descriptions are supported by observations, and how they can be used to characterize the underlying system. Here, we introduce a general framework for constructing constrained surrogates capable of representing arbitrary families of continuous distributions. We demonstrate its utility by providing explicit algorithms for several canonical distributions in statistical physics, including continuous powerlaw, lognormal, exponential, and truncated Gaussian distributions. These constrained surrogates enable unbiased estimation and accurate tests of model validity based on arbitrary (physically meaningful) sample statistics, without requiring specification or estimation of model parameters. We show how these theoretical advantages translate into more informative and nuanced conclusions in applications ranging from bushfire magnitudes and word usage in texts to brain connectomes and city populations.
Versions
Related
- Reliable Hybrid Neural Surrogates for Multidimensional Grids: Application to Double Parton Distributions
- Modified Family-Vicsek Scaling and Probability Distributions for Brownian Castle Interfaces
- Real-time Tunable Probability Distributions From Perimeter-Gated SPAD TRNGs
- Tensor Network Moral Graph Recovery of Discrete Probability Distributions
- A flux-balanced diffuse-interface kinetic model for rarefied gas-solid boundaries with arbitrary absorption probability
BibTeX
@misc{moore2026constrained,
title = {{Constrained surrogates for arbitrary families of continuous probability distributions}},
author = {Jack Murdoch Moore and Eduardo G Altmann},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.31695},
eprint = {2609.31695},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.31695},
}
RIS
TY - UNPB
TI - Constrained surrogates for arbitrary families of continuous probability distributions
AU - Jack Murdoch Moore
AU - Eduardo G Altmann
PY - 2026
DA - 2026/09/18
PB - arXiv
DO - 10.48550/arxiv.2609.31695
UR - https://arxiv.org/abs/2609.31695
AB - Empirical regularities described by parametrized families of probability distributions can shape how complex systems are interpreted and explained. A recurring problem is to determine the extent to which these descriptions are supported by observations, and how they can be used to characterize the underlying system. Here, we introduce a general framework for constructing constrained surrogates capable of representing arbitrary families of continuous distributions. We demonstrate its utility by providing explicit algorithms for several canonical distributions in statistical physics, including continuous powerlaw, lognormal, exponential, and truncated Gaussian distributions. These constrained surrogates enable unbiased estimation and accurate tests of model validity based on arbitrary (physically meaningful) sample statistics, without requiring specification or estimation of model parameters. We show how these theoretical advantages translate into more informative and nuanced conclusions in applications ranging from bushfire magnitudes and word usage in texts to brain connectomes and city populations.
ER -