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667-per-cm.net | ||
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gregorygundersen.com
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| | | | | [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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weisser-zwerg.dev
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| | | | | A series about Monte Carlo methods and generating samples from probability distributions. | |
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erikbern.com
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| | | | | 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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wwwtyro.net
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| | | [AI summary] The provided text is a detailed explanation of a fragment shader implementation for path tracing in a WebGL application. It includes code for rendering a caffeine molecule, using ping-pong framebuffers for accumulation, and displaying the final result. The explanation covers the ray-sphere intersection, ray-plane intersection, and the overall structure of the shader program. The text also includes functions for resetting and resizing the canvas, as well as a loop for continuous rendering. | ||
