A Conceptual Introduction to Hamiltonian Monte Carlo
2017/01/10 by Michael Betancourt, Betancourt, Michael · 7 voices · 135 citations
Mathematics · #Markov Chains and Monte Carlo Methods #Mathematical Approximation and Integration #Stochastic processes and statistical mechanics
paper · pdf · doi:10.48550/arxiv.1701.02434
Abstract
Hamiltonian Monte Carlo has proven a remarkable empirical success, but only recently have we begun to develop a rigorous understanding of why it performs so well on difficult problems and how it is best applied in practice. Unfortunately, that understanding is confined within the mathematics of differential geometry which has limited its dissemination, especially to the applied communities for which it is particularly important. In this review I provide a comprehensive conceptual account of these theoretical foundations, focusing on developing a principled intuition behind the method and its optimal implementations rather of any exhaustive rigor. Whether a practitioner or a statistician, the dedicated reader will acquire a solid grasp of how Hamiltonian Monte Carlo works, when it succeeds, and, perhaps most importantly, when it fails.
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Discussions
- A Conceptual Introduction to Hamiltonian Monte Carlo [hn, 155 points, 33 comments]
- Overview of differential geometry for Hamiltonian Monte Carlo [hn, 8 points, 0 comments]
- A Conceptual Introduction to Hamiltonian Monte Carlo [lobsters, 5 points, 1 comments]
- A Conceptual Introduction to Hamiltonian Monte Carlo [pdf] [hn, 1 points, 0 comments]
- Hamiltonian Monte Carlo for practitioners (light on differential geometry rigor, heavy on nice cartoons) https://arxiv.org/abs/1701.02434 [bsky, 0 points, 0 comments]
- Experiential learning of Hamiltonian Monte Carlo while skiing. I SHALL EMBODY THE FRICTIONLESS PARTICLE! (reference: arxiv.org/abs/1701.02434 [bsky, 0 points, 1 comments]
- Much of @betanalpha's great #stancon2017 talk comes from his recent paper on arXiv: arxiv.org/abs/1701.02434 [bsky, 0 points, 0 comments]
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