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

TL;DR

This paper presents a new information geometric method for efficiently constructing exact confidence regions in non-linear models, with applications in cosmology and epidemic modeling, and provides an open-source implementation.

Contribution

It introduces a novel information geometric approach to precisely determine confidence regions for non-linear models, enabling efficient construction of confidence bands with minimal extra computation.

Findings

Exact confidence regions can be constructed efficiently using the proposed method.

The approach is demonstrated with real-world examples in cosmology and epidemic modeling.

An open-source Julia package implements the methods for broader use.

Abstract

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.