022807 - Lecture 11 Recal l Getting to Metropolis algorithm...

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Unformatted text preview: Lecture 11: 02/28/2007 Recal l: Getting to Metropolis algorithm Problem: X= phase space for a physical system of “many particles” (huge) Have a probability distribution on states: Boltzmann or Gibbs distribution: =-∈( ) px C0e x kT • T=temp • K=Boltzmann’s constant • (x)=??? Of states Є Want to “draw a sample according to p(x)”—ie. Generate a population of points in X distributed roughly according to p(x). (Rationale : good for computing E p (f(x)) where f(x) is a “physical variable of interest” by SLLN) P(x) might be like (for some given T). Figure1 Intuitively want population to be concentrated under peaks in p(x). To understand algorithm better, imagine we’re working with a fixed discretization of X—call the set of points in discretization S. Metropolis Algorithm : pick some point in S j call it Θ D . Go to step (1); store Θ in P(a big multi-set of points in X) 1. Assume you have Θ m . From Ψ m by perturbing Θ m according to a uniform * random variable.random variable....
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This note was uploaded on 09/14/2007 for the course ECE 496 taught by Professor Delchamps during the Spring '07 term at Cornell.

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022807 - Lecture 11 Recal l Getting to Metropolis algorithm...

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