# On Probability and Cosmology: Inference Beyond Data?

## TL;DR

This paper discusses the limitations of traditional Bayesian inference in cosmology, especially for the universe as a whole, and proposes a generalized framework incorporating model structure and values for rational model assessment.

## Contribution

It introduces a novel axiological Bayesian framework that extends inference beyond empirical data by including model properties like elegance and beneficence.

## Key findings

- Traditional Bayesian methods struggle with the universe's global properties.
- Implicit valuations affect model assessment in cosmology.
- A generalized lattice-based Bayesian framework is proposed.

## Abstract

Modern scientific cosmology pushes the boundaries of knowledge and the knowable. This is prompting questions on the nature of scientific knowledge. A central issue is what defines a 'good' model. When addressing global properties of the Universe or its initial state this becomes a particularly pressing issue. How to assess the probability of the Universe as a whole is empirically ambiguous, since we can examine only part of a single realisation of the system under investigation: at some point, data will run out. We review the basics of applying Bayesian statistical explanation to the Universe as a whole. We argue that a conventional Bayesian approach to model inference generally fails in such circumstances, and cannot resolve, e.g., the so-called 'measure problem' in inflationary cosmology. Implicit and non-empirical valuations inevitably enter model assessment in these cases. This undermines the possibility to perform Bayesian model comparison. One must therefore either stay silent, or pursue a more general form of systematic and rational model assessment. We outline a generalised axiological Bayesian model inference framework, based on mathematical lattices. This extends inference based on empirical data (evidence) to additionally consider the properties of model structure (elegance) and model possibility space (beneficence). We propose this as a natural and theoretically well-motivated framework for introducing an explicit, rational approach to theoretical model prejudice and inference beyond data.