Markov chain Monte CarloJacob Jackson
Introduction• Metropolis algorithm for Monte Carlo
• Simplex method for linear
programming
• Krylov subspace iteration methods
• The decompositional approach to
matrix computations
• The Fortran optimizing compiler
• QR algorithm for computing
eigenvalues
• Quicksort algorithm for sorting
• Fast Fourier transform
• Integer relation detection
• Fast multipole method
Introduction• Metropolis algorithm for Monte Carlo
• Simplex method for linear
programming
• Krylov subspace iteration methods
• The decompositional approach to
matrix computations
• The Fortran optimizing compiler
• QR algorithm for computing
eigenvalues
• Quicksort algorithm for sorting
• Fast Fourier transform
• Integer relation detection
• Fast multipole method
Motivating example: Bayesian inference
Motivating example: Bayesian inference
Motivating example: Bayesian inference
Motivating example: Bayesian inference
Motivating example: Bayesian inference
Motivating example: Bayesian inference
Motivating example: Bayesian inference
Motivating example: Bayesian inference
Motivating example: Bayesian inference
Motivating example: Bayesian inference
Motivating example: Bayesian inference
Motivating example: Bayesian inference
Motivating example: Bayesian inference
Motivating example: Bayesian inference
Motivating example: Bayesian inference
Motivating example: Bayesian inference
Motivating example: Bayesian inference
Problem formulation
Problem formulation
Problem formulation
Problem formulation
Problem formulation
Problem formulation
Problem formulation
Simple solution
Simple solution
Simple solution
Simple solution
Simple solution
Metropolis-Hastings algorithm history
Metropolis-Hastings algorithm
Metropolis-Hastings algorithm
Metropolis-Hastings algorithm
Metropolis-Hastings algorithm
https://chi-feng.github.io/mcmc-demo/app.html#RandomWalkMH,banana
“Proof” of correctness for Metropolis-Hastings
“Proof” of correctness for Metropolis-Hastings
“Proof” of correctness for Metropolis-Hastings
“Proof” of correctness for Metropolis-Hastings
“Proof” of correctness for Metropolis-Hastings
“Proof” of correctness for Metropolis-Hastings
“Proof” of correctness for Metropolis-Hastings
“Proof” of correctness for Metropolis-Hastings
“Proof” of correctness for Metropolis-Hastings
“Proof” of correctness for Metropolis-Hastings
“Proof” of correctness for Metropolis-Hastings
“Proof” of correctness for Metropolis-Hastings
“Proof” of correctness for Metropolis-Hastings
“Proof” of correctness for Metropolis-Hastings
“Proof” of correctness for Metropolis-Hastings
“Proof” of correctness for Metropolis-Hastings
“Proof” of correctness for Metropolis-Hastings
What does M-H do, again?
Bayesian inference
Non-toy example
Connection with optimization
Note
Some links for those interested
http://www.jmlr.org/papers/volume3/blei03a/blei03a.pdf
https://arxiv.org/abs/1704.03581
https://www.coursera.org/learn/bayesian