Markov chain Monte Carlo | Monte Carlo methods
The Hamiltonian Monte Carlo algorithm (originally known as hybrid Monte Carlo) is a Markov chain Monte Carlo method for obtaining a sequence of random samples which converge to being distributed according to a target probability distribution for which direct sampling is difficult. This sequence can be used to estimate integrals with respect to the target distribution (expected values). Hamiltonian Monte Carlo corresponds to an instance of the Metropolis–Hastings algorithm, with a Hamiltonian dynamics evolution simulated using a time-reversible and volume-preserving numerical integrator (typically the leapfrog integrator) to propose a move to a new point in the state space. Compared to using a Gaussian random walk proposal distribution in the Metropolis–Hastings algorithm, Hamiltonian Monte Carlo reduces the correlation between successive sampled states by proposing moves to distant states which maintain a high probability of acceptance due to the approximate energy conserving properties of the simulated Hamiltonian dynamic when using a symplectic integrator. The reduced correlation means fewer Markov chain samples are needed to approximate integrals with respect to the target probability distribution for a given Monte Carlo error. The algorithm was originally proposed by Simon Duane, Anthony Kennedy, Brian Pendleton and Duncan Roweth in 1987 for calculations in lattice quantum chromodynamics. In 1996, Radford M. Neal brought attention to the usefulness of the method for a broader class of statistical problems, in particular artificial neural networks. The burden of having to supply gradients of the respective densities delayed the wider adoption of the method in statistics and other quantitative disciplines, until in the mid-2010s the developers of Stan implemented HMC in combination with automatic differentiation. (Wikipedia).
Moving on from Lagrange's equation, I show you how to derive Hamilton's equation.
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Joan ELIAS MIRÓ - Precise calculations with the Renormalized Hamiltonian Truncation approach
https://indico.math.cnrs.fr/event/2435/
From playlist Workshop “Hamiltonian methods in strongly coupled Quantum Field Theory”
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From playlist Summer of Math Exposition 2 videos
Hamiltonian Cycles, Graphs, and Paths | Hamilton Cycles, Graph Theory
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Hamiltonian Simulation and Universal Quantum (...) - T. Cubitt - Main Conference - CEB T3 2017
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From playlist 2017 - T3 - Analysis in Quantum Information Theory - CEB Trimester
How To Derive The Hamiltonian From The Lagrangian Like a Normie
I made a video on how to convert from lagrangian to hamiltonian: https://www.youtube.com/watch?v=0H9T2_dMfW8&t=2s Now I actually derive the relationship! Interested in tutoring? Check out the following link: dotsontutoring.simplybook.me or email dotsontutoring.gmail.com
From playlist Math/Derivation Videos
John HILLER - Nonperturbative light-front methods
https://indico.math.cnrs.fr/event/2435/
From playlist Workshop “Hamiltonian methods in strongly coupled Quantum Field Theory”
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Andreas LÄUCHLI - Numerical Hamiltonian truncation approach to the \phi^4 theory in 1+1d and beyond
https://indico.math.cnrs.fr/event/2435/
From playlist Workshop “Hamiltonian methods in strongly coupled Quantum Field Theory”
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AQC 2016 - Adiabatic Quantum Computer vs. Diffusion Monte Carlo
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Statistical Rethinking - Lecture 11
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From playlist Statistical Rethinking Winter 2015
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Graph Theory: 27. Hamiltonian Graphs and Problem Set
I define a Hamilton path and a Hamilton cycle in a graph and discuss some of their basic properties. Then I pose three questions for the interested viewer. Solutions are in the next video. An introduction to Graph Theory by Dr. Sarada Herke. Related Videos: http://youtu.be/3xeYcRYccro -
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