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\centerline{\ssb  Syllabus -- ISC 5228 Markov Chain Monte Carlo Simulations}
\centerline{\ssb  Fall Semester 2008}
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{\ssi Instructor:}\quad Prof. Bernd A. Berg, 615 Keen (Physics),
phone 644--6246 or -1492 \medskip
{\ssi Meeting times:}\quad T R 3:35-4:50 pm, 152 DSL. Office hours:
See course website.
\medskip
{\ssi Credit:}\quad 3 hours.   \medskip
{\ssi Prerequisites: \quad}  Calculus I and II, or consent of the 
instructor. A basic knowledge of Fortran~77 is disireable, but 
can also be aquired during the course.
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\noindent
{\ssi Course Description:}
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 \ssf
 With the emergence of high performance computing simple Monte
 Carlo (MC) and Markov Chain Monte Carlo (MCMC) simulations have
 become a major enabling technique in
 applied sciences.  The goal of this course is to provide a
 self-contained presentation.  This includes not only Monte Carlo
 methods themselves, but also its statistical foundations and the
 statistics needed to analyze MCMC data, which are autocorrelated.
 The course is addressed to applied scientists, who need ``ready to
 work recipes'' and running computer code (which will be provided for all
 subjects covered).  Illustrative examples may be drawn from statistical
 physics or from topics of other participating departments, for instance
 from simulations of biomolecules. Students are encouraged to bring in 
 their own examples, related to their planned or actual research work.
 \bigskip

\noindent
{\ssi Text (required):}
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Markov Chain Monte Carlo Simulations and Their Statistical Analysis
(With Web-Based Fortran Code), Bernd A. Berg, World Scientific 2004,
ISBN 981-238-935-0.
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\noindent
{\ssi Alternate Texts (not required):}
\medskip

Markov Chain Monte Carlo: Innovations and Applications (Lecture Notes
Series, Institute for Mathematical Sciences, National University of
Singapore, Vol.~7), W.S. Kendall, F. Liang, and J.-S. Wang, World
Scientific 2005, ISBN 981-256-427-6.
\medskip

Markov Chain Monte Carlo in Practice -- Interdisciplinary Statistics,
W.R. Gilks, S. Richardson and D.J. Spiegelhalter, Chapman and Hall/CRC,
1996, ISBN 041-205-551-1.
\medskip

A Guide to Monte Carlo Simulations in Statistical Physics, David
Landau and Kurt Binder, Cambridge University Press, 2000, ISBN
052-165-366-5.
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Monte Carlo Strategies in Scientific Computing (Springer Series in
Statistics), Jun S. Liu, Springer, 2001, ISBN 038-795-230-6.
\bigskip

\noindent
{\ssi Objectives:}
\medskip

The students should become able to implement the methods in their own
computer programs and to apply them to their own research projects.
Towards the end of the semester each student will have to demonstrate
her or his understanding by presenting a final project to the class.
On the way to the goal that the students use MCMC simulations in own 
research, there will be numerous assignments, which define and test 
the required skills. In particular the assignments will include 
(but are not be limited to):
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\item{-} Install and run pseudo-random number generators to
         generate distribution functions.
         % probability densities and cumulative 
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\item{-} Make graphical illustration (e.g., gnuplot).
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\item{-} Apply difference tests (Gaussian, Student, F-Test)
         to estimators of suitable random variables.
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\item{-} Perform MC simulations and estimate their confidence 
         bounds.
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\item{-} Use MPI (Message Passing Interface) for parallel MC
         simulations. 
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\item{-} Bootstrap confidence limits of statistical investigations.
\smallskip

\item{-} Set up MCMC simulations using the Metropolis, the heatbath
         or other suitable updating schemes.
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\item{-} Illustrate ``self-averaging'' of MCMC data with a least on
         example from statistical physics.
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\item{-} Re-weight MCMC data.
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\item{-} Perform jackknife error bar calculations.
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\item{-} Calculate autocorrelations and the integrated autocorrelation
         times for MCMC data and be able to explain the difference 
         between self-consistent and ``reasonable'' error analysis 
         of MCMC data.
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\item{-} Evaluate the efficiency of distinct MCMC updating schemes
         against one another.
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\item{-} Determine fit parameters from independent data of MCMC
         simulations.
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\item{-} Determine fit parameters from autocorrelated data of MCMC
         simulations.
\smallskip

\item{-} Be able to give an overview of applications of MCMC
         simulations.
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\noindent
{\ssb  Outline:}
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The corresponding chapters of the book will be reading assignments
as posted on the web. 

The actual order of topics may be different from the one listed below.
\medskip

\item{1.}\quad Sampling, statistics and computer code (5 lectures)

\itemitem{-} probability distributions, sampling and random numbers
\itemitem{-}  organization of the computer code
\itemitem{-}  Gaussian distribution
\itemitem{-}  confidence intervals
\itemitem{-}  order statistics and heapsort
\itemitem{-}  MC simulations and bootstraping of 
\itemitem{-}  Bootstrapping of confidence limits of statistical 
              investigations
\itemitem{-}  functions and expectation values of random variables
\itemitem{-}  sums of independent random variables and characteristic
              functions
% \itemitem{-}  linear transformation of random variables
\itemitem{-}  the central limit theorem and binning

 \item{2.}\quad Error analysis for independent random variables (4 lectures)

\itemitem{-}  Gaussian confidence intervals and error bars
\itemitem{-}  estimators of the variance and bias
\itemitem{-}  statistical error bar routines
\itemitem{-}  the Gaussian difference test
\itemitem{-}  the $\chi^2$ and sample variance distribution
\itemitem{-} Gosset's student distribution and student difference test
\itemitem{-} the error of the error bar and the variance ratio test
             (F-test)
\itemitem{-}  When are distributions consistent? ($\chi^2$ and
              Kolmogorov tests)
\itemitem{-}  The jackknife approach
\itemitem{-}  determination of parameters (linear and
              Levenberg-Marquardt fitting)

\item{3.}\quad  Markov Chain Monte Carlo (6 lectures)

\itemitem{-}  preliminaries: The canonical ensemble and the
              two-dimensional Ising model
\itemitem{-}  lattice labeling
\itemitem{-}  sampling and re-weighting
\itemitem{-}  importance sampling
\itemitem{-}  the Metropolis algorithm
\itemitem{-}  the heath bath algorithm
\itemitem{-}  illustrations of Monte Carlo simulations I:
              discrete systems
\itemitem{-}  illustrations of Monte Carlo simulations II:
              continuous systems

\item{4.}\quad  Error analysis for Markov chain data (5 lectures)

 \itemitem{-} autocorrelations
 \itemitem{-} integrated autocorrelation time and binning
% \itemitem{-}  self-consistent versus reasonable error analysis
 \itemitem{-} analysis of MCMC data (examples)
 \itemitem{-} comparison of MCMC algorithms
\itemitem{-}  fitting of MCMC data

\item{5.}\quad  Advanced Topics (6 lectures, the instructor will 
                choose a subset)

\itemitem{-}  simulations of generalized ensembles
\itemitem{-}  free energy and entropy calculations
\itemitem{-}  event driven simulations
\itemitem{-}  cluster algorithms
% \itemitem{-}  hybrid Monte Carlo \itemitem{-}  kinetic Monte Carlo
% \itemitem{-}  large scale simulations
\itemitem{-}  replica exchange method with MPI
\itemitem{-}  checkerboard algorithms with MPI
\itemitem{-}  {\ssb to be announced (may be influenced by students)}

\item{6.}\quad  Presentation of Final Projects (5 lectures, starting 
                whenever the first project is ready)

The estimates of the numbers of lectures are approximate and include 
time for tests and discussions.
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\noindent
{\ssb Grading/Evaluation:}

The course grade will be based to 70\% on assignments (mainly
computational) and to 30\% on a final project, which each student
is expected to present in class. Regular class attendance is required.
At least half of the assignments will be given unannounced during 
class hours and a score of zero points will be recorded if you are 
absent without a legitimate excuse. The other assignments will be 
given as homework. The topic of the final project should be discussed 
with the instructor and be decided by the eighth week or earlier. 
This includes mandatory visits of the office hours of the instructor. 
Projects which relate MCMC calculations to your actual research are 
most desireable.
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The course grade dividing lines are: $A>90\%,\  A^->85\%,\
B^+>80\%,\ B>70\%,\ B^->65\%,\ C^+>60\%,\ C>50\%,\ C^->45\%,\
D>30\%$ and $F$ for less or equal $30\%$.
\bigskip

\noindent {\ssb Honor Code: }
A copy of the University Academic
Honor Code can be found in the current Student Handbook. You are
bound by this in all of your academic work. It is based on the
premise that each student has the responsibility 1) to uphold the
highest standards of academic integrity in the students own work,
2) to refuse to tolerate violations of academic integrity in the
University community, and 3) to foster a high sense of integrity
and social responsibility on the part of the University community.
Out of class you are encouraged to work together on assignments
but plagiarizing of the work of others or study manuals is
academically dishonest. 
% Please see the following web site for a
% complete explanation of the Academic Honor Code.
% http://www.fsu.edu/Books/Student-Handbook/codes/honor.html
% http://www.fsu.edu/Books/Student-Handbook/

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\noindent {\ssb ADA:} Students with disabilities needing academic
accommodations should: 1) register with and provide documentation
to the Student Disability Resource Center (SDRC); 2) bring a
letter to the instructor from SDRC indicating you need academic
accommodations. This should be done within the first of class.
This and other class materials are available in alternative format
upon request.

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{\ssb See the FSU website on Teaching Policies, as linked on the course 
hompage for these and other relevant FSU Teaching Policies in their 
up-to-date version.}

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