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