Markov chain Monte Carlo | Monte Carlo methods

Hamiltonian Monte Carlo

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).

Video thumbnail

A09 The Hamiltonian

Moving on from Lagrange's equation, I show you how to derive Hamilton's equation.

From playlist Physics ONE

Video thumbnail

Hamiltonian Mechanics in 10 Minutes

In this video I go over the basics of Hamiltonian mechanics. It is the first video of an upcoming series on a full semester university level Hamiltonian mechanics series. Corrections -4:33 the lagrangian should have a minus sign between the first two terms, not a plus.

From playlist Summer of Math Exposition 2 videos

Video thumbnail

Hamiltonian Cycles, Graphs, and Paths | Hamilton Cycles, Graph Theory

What are Hamiltonian cycles, graphs, and paths? Also sometimes called Hamilton cycles, Hamilton graphs, and Hamilton paths, we’ll be going over all of these topics in today’s video graph theory lesson! A Hamilton cycle in a graph G is a cycle containing all vertices of G. A Hamilton path

From playlist Graph Theory

Video thumbnail

Hamiltonian Simulation and Universal Quantum (...) - T. Cubitt - Main Conference - CEB T3 2017

Toby Cubitt (UCL) / 14.12.2017 Title: Hamiltonian Simulation and Universal Quantum Hamiltonians Abstract: Physical (or "analogue") Hamiltonian simulation involves engineering a Hamiltonian of interest in the laboratory, and studying its properties experimentally (somewhat analogous to b

From playlist 2017 - T3 - Analysis in Quantum Information Theory - CEB Trimester

Video thumbnail

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

Video thumbnail

Graph Theory: Hamiltonian Graphs

This video is about Hamiltonian graphs and some of their basic properties.

From playlist Basics: Graph Theory

Video thumbnail

SLT Supplemental - Seminar 2 - Markov Chain Monte Carlo

This series provides supplemental mathematical background material for the seminar on Singular Learning Theory. In this seminar Liam Carroll introduces us to Markov Chain Monte Carlo, a method for sampling from the Bayesian posterior. The webpage for this seminar is http://metauni.org/pos

From playlist Metauni

Video thumbnail

AQC 2016 - Adiabatic Quantum Computer vs. Diffusion Monte Carlo

A Google TechTalk, June 29, 2016, presented by Stephen Jordan (NIST) ABSTRACT: While adiabatic quantum computation using general Hamiltonians has been proven to be universal for quantum computation, the vast majority of research so far, both experimental and theoretical, focuses on stoquas

From playlist Adiabatic Quantum Computing Conference 2016

Video thumbnail

Thermal properties of frustrated quantum magnets by Frederic Mila

PROGRAM FRUSTRATED METALS AND INSULATORS (HYBRID) ORGANIZERS: Federico Becca (University of Trieste, Italy), Subhro Bhattacharjee (ICTS-TIFR, India), Yasir Iqbal (IIT Madras, India), Bella Lake (Helmholtz-Zentrum Berlin für Materialien und Energie, Germany), Yogesh Singh (IISER Mohali, In

From playlist FRUSTRATED METALS AND INSULATORS (HYBRID, 2022)

Video thumbnail

Statistical Rethinking Fall 2017 - week06 lecture10

Week 06, lecture 10 for Statistical Rethinking: A Bayesian Course with Examples in R and Stan, taught at MPI-EVA in Fall 2017. This lecture covers Chapter 8. Slides are available here: https://speakerdeck.com/rmcelreath Additional information on textbook and R package here: http://xcel

From playlist Statistical Rethinking Fall 2017

Video thumbnail

AQC 2016 - Scaling Analysis & Instantons for Thermally-Assisted Tunneling and Quantum MC Simulations

A Google TechTalk, June 28, 2016, presented by Zhang Jiang (NASA) ABSTRACT: We develop an instantonic calculus to derive an analytical expression for the thermally-assisted tunneling decay rate of a metastable state in a fully connected quantum spin model. The tunneling decay problem can

From playlist Adiabatic Quantum Computing Conference 2016

Video thumbnail

Statistical Rethinking 2022 Lecture 08 - Markov chain Monte Carlo

Slides and other course materials: https://github.com/rmcelreath/stat_rethinking_2022 Music: Intro: https://www.youtube.com/watch?v=E06X1NXRdR4 Skate1 vid: https://www.youtube.com/watch?v=GCr0EO41t8g Skate1 music: https://www.youtube.com/watch?v=o3WvAhOAoCg Skate2 vid: https://www.youtube

From playlist Statistical Rethinking 2022

Video thumbnail

Statistical Rethinking - Lecture 11

Lecture 11 - Markov chain Monte Carlo - Statistical Rethinking: A Bayesian Course with R Examples

From playlist Statistical Rethinking Winter 2015

Video thumbnail

Statistical Rethinking Winter 2019 Lecture 10

Lecture 10 of the Dec 2018 through March 2019 edition of Statistical Rethinking: A Bayesian Course with R and Stan. This lecture covers Chapter 9, Markov Chain Monte Carlo.

From playlist Statistical Rethinking Winter 2019

Video thumbnail

Iterative stochastic numerical methods for statistical sampling: Professor Ben Leimkuhler

I study the design, analysis and implementation of algorithms for time-dependent phenomena and modelling for problems in engineering and the sciences. My previous works have helped to establish the foundations of molecular simulation, providing efficient deterministic and stochastic numeri

From playlist Data science classes

Video thumbnail

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 -

From playlist Graph Theory part-5

Related pages

Symplectic integrator | Automatic differentiation | Metropolis-adjusted Langevin algorithm | Stan (software) | Convergence of random variables | Hamiltonian mechanics | Gradient | Probability density function | Monte Carlo integration | Momentum | Markov chain Monte Carlo | Metropolis–Hastings algorithm | Position (geometry) | Leapfrog integration | List of software for Monte Carlo molecular modeling | Random walk | Markov chain | Probability distribution | Normal distribution | Time reversibility | Harmonic oscillator | Artificial neural network | Dynamic Monte Carlo method | Random variable | Sampling (statistics) | Conservation of energy | Binary tree