For the same data set: Use the jackknife method to calculate the biascorrected estimator and its errorbar for
xi exp( xi )
.
x( ) = i
i exp( xi )
Choose 0 10 and plot 100 estimates of this function with their error
bars. E-mail the plot to the instructor.
Simple MC Integration
Use MC to calculate the integrals
I1 =
dx dy .
x2 <sin(y ),y 2 <cos(x)
and
dx dy er , r =
I2 =
x2 + y 2 .
x2 <sin(y ),y 2 <cos(x)
Make a scatter plot of the contributing integrand range. E-mail your
program, the results for the integ
Biased Metropolis-Heatbath
Algorithm
Alexei Bazavov
Florida State University
November 2005
Introduction
In the Metropolis procedure transition probability from the
conguration (k ) to (l) is given as
W (l)(k) = f (l, k ) w(l)(k) for l = k
W (k) (k ) = f (
Path Integral Monte Carlo
Keola Wierschem
Physics Department, FSU
Path Integral Monte Carlo p. 1/
What is Path Integral Monte Carlo?
A computational technique for simulating quantum
systems at non-zero temperature.
PIMC allows us to use particle interacti
Pairing instability of composite fermions in double layer quantum Hall system
Huan D. Tran
Quantum Hall effect Composite fermion FQHE in double layer electron system Proposal work
04/30/09
FSU Physics Department
1
Quantum Hall Effect
E x xx = E y yx
x
Pseudorandom Number Generators and the Metropolis Algorithm
Jane Ren
Introduction to random number generators The Marsaglia random number generator SPRNG (A Scalable Library for Pseudorandom Number Generation) Textbook assignment 3.2.3 with Marsaglia ran
Lecture V: Multicanonical Simulations.
1. Multicanonical Ensemble
2. How to get the Weights?
3. Example Runs (2d Ising and Potts models)
4. Re-Weighting to the Canonical Ensemble
5. Energy and Specic Heat Calculation
6. Free Energy and Entropy Calculation
Contents of Lecturenotes IV
1. The O(3) Model and the Heat Bath Algorithm
1
The O(3) Model and the Heat Bath Algorithm
We give an example of a model with a continuous energy function. The 2d
version of the model is of interest to eld theorists because of
Contents of Lecture IV
1. Statistical Errors of Markov Chain MC Data
2. Autocorrelations
3. Integrated Autocorrelation Time and Binning
4. Illustration: Metropolis generation of normally distributed data
5. Self-consistent versus reasonable error analysis
Contents of Lecture III
1. The Central Limit Theorem and Binning
2. Gaussian Error Analysis for Large and Small Samples
3. The Jackknife Approach
1
The Central Limit Theorem and Binning
How is the sum of two independent random variables
y r = xr + xr .
1
Contents of Lecturenotes II
1. Statistical Physics and Potts Models
2. Sampling and Re-weighting
3. Importance Sampling and Markov Chain Monte Carlo
4. The Metropolis Algorithm
1
Statistical Physics and Potts Model
MC simulations of systems described by t
Lecturenotes MCMC IV Contents
1. Multicanonical Ensemble
2. How to get the Weights?
3. Example Runs (2d Ising and Potts models)
4. Re-Weighting to the Canonical Ensemble
5. Energy and Specic Heat Calculation
6. Free Energy and Entropy Calculation
7. Summa
The Jackknife Approach
Jackknife estimators allow to correct for a bias and its statistical error. The
method was introduced in the 1950s in papers by Quenouille and Tukey. The
jackknife method is recommended as the standard for error bar calculations. In
MCMC Course Fall 2005
Due November 3
Use the subroutine gau metro.f for the Metropolis generation of Gaussian random numbers. Report the acceptance rates and estimate the integrated autocorrelation time from a time series of 2*21 numbers.
If you personal
Simple MC Integration
Use MC to calculate the integrals
I1 =
dx dy .
x2 <sin(y ),y 2 <cos(x)
and
dx dy er , r =
I2 =
x2 + y 2 .
x2 <sin(y ),y 2 <cos(x)
Make a scatter plot of the contributing integrand range. E-mail your
program, the results for the integ