Chapter 3 Markov Chain Monte Carlo Metropolis and

Contents • Reminders from previous weeks • Definitions • Theorems • Motivation • Metropolis

Glauber Dynamics (Gibbes sampler) v is vacant If x(v)=1 y=x

Summary Chain construction with a given stationary distribution • Metropolis – given a transition

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Chapter 3 Markov Chain Monte Carlo: Metropolis and Glauber Chains Yael Harel

Contents • Reminders from previous weeks • Definitions • Theorems • Motivation • Metropolis Chains • What is it? • Construction over symmetric matrices • Example • Construction over asymmetric matrices • Example • Glauber Dynamics • What is it? • Examples • Metropolis Chains VS Glauber Dynamics • Summary

Reminders from previous weeks

Motivation e asy d ult c i iff

Metropolis Chains

Glauber Dynamics (Gibbes sampler)

Glauber Dynamics (Gibbes sampler) 0 0

Glauber Dynamics (Gibbes sampler) v is vacant If x(v)=1 y=x

Metropolis Chains VS Glauber Dynamics

Summary Chain construction with a given stationary distribution • Metropolis – given a transition matrix. • Glauber – without any transition matrix. Can be equal or similar Example – q-coloring • NP-complete problem #proper configurations – unknown. • Construct a chain with the uniform stationary distribution. • Simulation: • For i=1 to N • Run the chain T iterations • Save the result • Learn how does the configurations distribute In the next weeks: How to find T?

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