Archive for December 12, 2018

On Probability and Cosmology

Posted in The Universe and Stuff with tags , , , on December 12, 2018 by telescoper

I just noticed a potentially interesting paper by Martin Sahlén on the arXiv. I haven’t actually read it yet, so don’t know if I agree with it, but thought I’d point it out here for those interested in cosmology and things Bayesian.

Here is the 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.

You can download a PDF of the paper here.

As usual, comments are welcome below. I’ll add my thoughts later, after I’ve had the chance to read the article!

 

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