Incomplete Reparameterizations and Equivalent Metrics
Abstract
Reparameterizing a probabilisitic system is common advice for improving the performance of a statistical algorithm like Markov chain Monte Carlo, even though in theory such reparameterizations should leave the system, and the performance of any algorithm, invariant. In this paper I show how the reparameterizations common in practice are only incomplete reparameterizations which result in different interactions between a target probabilistic system and a given algorithm. I then consider how these changing interactions manifest in the context of Markov chain Monte Carlo algorithms defined on Riemannian manifolds. In particular I show how any incomplete reparameterization is equivalent to modifying the metric geometry directly.
- Publication:
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arXiv e-prints
- Pub Date:
- October 2019
- DOI:
- 10.48550/arXiv.1910.09407
- arXiv:
- arXiv:1910.09407
- Bibcode:
- 2019arXiv191009407B
- Keywords:
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- Statistics - Other Statistics;
- Mathematical Physics
- E-Print:
- 34 pages, 15 figures