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Constructing Exact Confidence Regions on Parameter Manifolds of Non-Linear Models

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arxiv 2211.03421 v1 pith:4Y2MZZS6 submitted 2022-11-07 stat.ME physics.data-anstat.CO

Rafael Arutjunjan , Bjoern Malte Schaefer , Clemens Kreutz This is my paper · ORCID
classification stat.MEphysics.data-anstat.CO
keywords confidenceexactmodelsregionsadditionalallowsaroundavailable
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Using the mathematical framework of information geometry, we introduce a novel method which allows one to efficiently determine the exact shape of simultaneous confidence regions for non-linearly parametrised models. Furthermore, we show how pointwise confidence bands around the model predictions can be constructed from detailed knowledge of the exact confidence region with little additional computational effort. We exemplify our methods using inference problems in cosmology and epidemic modelling. An open source implementation of the developed schemes is publicly available via the InformationGeometry.jl package for the Julia programming language.

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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Compressed 'CMB-lite' Likelihoods Using Automatic Differentiation

    astro-ph.CO 2024-12 accept novelty 6.0 of 10

    An automatic differentiation scheme constructs CMB-lite likelihoods from one minimisation and one Hessian evaluation, reproducing full multi-frequency posterior constraints on SPT-3G data within 0.1 sigma.

  2. Partition function approach to non-Gaussian likelihoods: information theory and state variables for Bayesian inference

    cond-mat.stat-mech 2024-11 conditional novelty 5.0 of 10

    Bayesian updating is rewritten as a temperature-dependent partition function, yielding an effective dimension that quantifies how non-Gaussian a posterior is.

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