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

Parallel Computing
After briey discussing the often neglected, but in praxis frequently encountered, issue of trivially parallel computing, we turn to parallel computing with information exchange. Our illustration is the replica exchange method, also call

Lecturenotes 4 MCMC I Contents
1. Statistical Physics and Potts Models 2. Sampling and Re-weighting 3. Importance Sampling and Markov Chain Monte Carlo 4. The Metropolis Algorithm 5. The Heatbath Algorithm (Gibbs Sampler) 6. Start and Equilibration 7. Ene

Parallel Computing
After briefly discussing the often neglected, but in praxis frequently encountered, issue of trivially parallel computing, we turn to parallel computing with information exchange. Our illustration is the replica exchange method, also ca

Continuous Systems: Heisenberg Spin Model
We give an example of a model with a continuous energy function. The 2d version of the model is known as -model and of interest in field theory because of its analogies with 4d Yang-Mills theory. In statistical ph

Bayesian Statistics
Kolmogorov Axioms and Conditional Probabilities We denote events by A, B, C, . . . , and use the following notation: 1. A B = A and B, the event that A and B both occur. 2. Ac = not A, the event that A does not occur. 3. E, the event w

Lecturenotes 7 MCMC III Contents
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 erro

Message Passing Interface (MPI)
In a typical Unix installation a MPI Fortran 77 program will compile with . . . pathname/mpif77 O fln.f and generates an executable le, a.out, which runs with something like . . . pathname/mpirun nolocal np n a.out (2) (1)

Lecturenotes Statistics I Contents
1. Uniform and General Distributions
2. Condence Intervals, Cumulative Distribution Function and Sorting
1
Uniform and General Distributions
Uniform distribution (probability density):
u(x) =
1 for 0 x < 1;
0 elsewhere.

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

Random Number Generator of STMC and simple Monte Carlo Integration
Bernd Berg FSU MCMC Course, August 26, September 2, 2008
Random Numbers and Fortran Code
According to Marsaglia and collaborators a list of desirable properties for random number generator