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667-per-cm.net | ||
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gregorygundersen.com
[AI summary] Hamiltonian Monte Carlo (HMC) is a Markov Chain Monte Carlo (MCMC) method that leverages Hamiltonian dynamics to generate samples from a probability distribution. Unlike traditional MCMC methods that rely on random walks, HMC introduces auxiliary momenta variables and simulates a physical system to produce correlated samples with higher efficiency. The method uses gradient information of the log density to guide the sampling process, enabling faster exploration of the target distribution and higher acceptance rates. The implementation of HMC involves defining the potential and kinetic energy functions, performing leapfrog integration to approximate the Hamiltonian dynamics, and using the Metropolis-Hastings acceptance criterion. An example using... |
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darrenjw.wordpress.com
Yesterday there was an RSS Read Paper meeting for the paper Unbiased Markov chain Monte Carlo with couplings by Pierre Jacob, John O'Leary and Yves F. Atchadé. The paper addresses the bias in MCMC estimates due to lack of convergence to equilibrium (the "burn-in" problem), and shows how it is possible to modify MCMC algorithms... |
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erikbern.com
I made a New Year's resolution: every plot I make during 2018 will contain uncertainty estimates. Nine months in and I have learned a lot, so I put together a summary of some of the most useful methods. |
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ddarmon.github.io
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