A General Metric for Riemannian Hamiltonian Monte Carlo

A General Metric for Riemannian Hamiltonian Monte Carlo Michael Betancourt University College London August 30th, 2013 I’m going to talk about probability and geometry, but not information geometry! Instead our interest is Bayesian inference ⇡(✓|D) / ⇡(D|✓) ⇡(✓) Markov Chain Monte Carlo admits the practical analysis and manipulation of posteriors even in high dimensions Markov transitions can be though of as an “average” isomorphism that preserves a target distribution (⌦, B(⌦), ⇡) Markov transitions can be though of as an “average” isomorphism that preserves a target distribution (⌦, B(⌦), ⇡) ( , B( ), ) t : ⌦ ! ⌦, 8t 2 Markov transitions can be though of as an “average” isomorphism that preserves a target distribution ⇡T = ⇡ (⌦, B(⌦), ⇡) ( , B( ), ) t : ⌦ ! ⌦, 8t 2 Random Walk Metropolis and the Gibbs sampler have been the workhorse Markov transitions Random Walk Metropolis and the Gibbs sampler have been the workhorse Markov transitions T(✓, ✓0 ) = N ✓0 |✓, 2 min ✓ 1, ⇡(✓0 ) ⇡(✓) ◆ Random Walk Metropolis and the Gibbs sampler have been the workhorse Markov transitions a|✏ ⇠ Ber ✓ min ✓ 1, ⇡(✓