2019/10/09 by Michael Betancourt, Betancourt, Michael · 1 citation
Computer Science · Mathematics · #Topological and Geometric Data Analysis #Morphological variations and asymmetry #Bayesian Methods and Mixture Models
paper · pdf · doi:10.48550/arxiv.1910.09407
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.