ICFP Stat Physics 2016

From Werner KRAUTH

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* Week 2 (14 September 2016): Statistical inference * Week 2 (14 September 2016): Statistical inference
-** [http://www.lps.ens.fr/~krauth/images/9/9a/HW02_ICFP_2016.pdf Homework 02: From Maximum Likelihood to Bayes statistics] Useful programs:+** [http://www.lps.ens.fr/~krauth/images/9/9a/HW02_ICFP_2016.pdf Homework 02: From Maximum Likelihood to Bayes statistics] Useful program:
*** [[bayes_tank_problem_HW02_ICFP_2016.py| Bayes_tank.py: Bayesian approach to solving the German Tank problem]] *** [[bayes_tank_problem_HW02_ICFP_2016.py| Bayes_tank.py: Bayesian approach to solving the German Tank problem]]
 +
 +References for Week 2:
 +* L. Wasserman, "All of Statistics, A Concise Course in Statistical Inference" (Springer, 2005) part 2
 +* W. Krauth, "Statistical Mechanics: Algorithms and Computations" (Oxford, 2006) p. 58 only ;)
 +* B. Efron, "Maximum likelihood and decision theory" Ann. Statist., vol. 10, pp. 340-356, 06 1982.
 +* B. Efron, "Bootstrap methods: another look at the jackknife" The Annals of Statistics, pp. 1-26, 1979.
 +* P. Diaconis and B. Efron, "Computer intensive methods in statistics" Scientific American, vol. 248, no. 5, pp. 116-130, 1983.
 +
 +
 +
==Syllabus== ==Syllabus==

Revision as of 00:00, 14 September 2016

This is the homepage for the ICFP course: Statistical Physics: Concepts and Applications.

Lectures: Werner KRAUTH

Practicals & Homeworks: Maurizio FAGOTTI, Olga PETROVA

Look here for practical information

References for Week 2:

  • L. Wasserman, "All of Statistics, A Concise Course in Statistical Inference" (Springer, 2005) part 2
  • W. Krauth, "Statistical Mechanics: Algorithms and Computations" (Oxford, 2006) p. 58 only ;)
  • B. Efron, "Maximum likelihood and decision theory" Ann. Statist., vol. 10, pp. 340-356, 06 1982.
  • B. Efron, "Bootstrap methods: another look at the jackknife" The Annals of Statistics, pp. 1-26, 1979.
  • P. Diaconis and B. Efron, "Computer intensive methods in statistics" Scientific American, vol. 248, no. 5, pp. 116-130, 1983.



Syllabus

  • Week 1: Probability theory
    • Probabilities, probability distributions, sampling
    • Random variables
    • Expectations
    • Inequalities (Markov, Chebychev, Hoeffding)
    • Convergence of random variables (Laws of large numbers, CLT)
    • Lévy distributions
  • Week 2: Statistics (statistical inference, estimation, learning)
    • Point estimation, confidence intervals
    • Bootstrap
    • Method of moments
    • Maximum likelihood, Fisher information
    • Parametric Bootstrap
    • Bayes statistics
  • Week 3: Statistical mechanics and Thermodynamics
    • Rapid overview on the connection between statistical mechanics and thermodynamics
    • lightning review of ensembles and
    • lightning review of the main physical quantities (partition function, energy, free energy, entropy, chemical potential, correlation functions, etc).
  • Week 4: Physics in one dimension
    • One-dimensional hard spheres, virial expansion, partition function
    • One-dimensional Ising model
    • Transfer matrix
    • Kittel model
    • ~Chui-Weeks model: Infinite-dimensional transfer matrix
    • One-dimensional Ising model with 1/r^2 interactions
  • Week 5: Two-dimensional Ising model: From Ising to Onsager
    • Peierls argument, ~Kramers-Wannier relation
    • Two-dimensional transfer matrix (following Schultz et al)
    • ~Jordan-Wigner transformation
    • Free energy calculation
    • Spontaneous magnetization, zero-field susceptibility
    • Kaufman, ~Ferdinand-Fisher, Beale
  • Week 6: Two-dimensional Ising model: From Kac and Ward to Saul and Kardar
    • Van der Waerden, low-temperature and high-temperature expansions
    • Duality
  • Week 7: Physics in two dimensions (~Kosterlitz-Thouless physics): XY (planar rotor) model
    • Peierls argument
    • ~Mermin-Wagner theorem
    • Non-universality
  • Week 8: Physics in two dimensions (~Kosterlitz-Thouless physics): Particle systems, superfluids
  • Week 09: Physics in infinite dimensions: Mean-field theory, Scaling
  • Week 10: Physics in infinite dimensions: Landau theory
  • Week 11: Renormalization group
  • Week 12: The Solid state: Order parameters, correlation functions
  • Week 13: Quantum systems - bosons.
  • Week 14: Quantum systems - spin systems
  • Week 15: Equilibrium and transport, Fluctuation-dissipation theorem.

References

Lecture notes will be available before each course.

Books

  • L. Wasserman, "All of Statistics, A Concise Course in Statistical Inference" (Springer, 2005)
  • W. Krauth, "Statistical Mechanics: Algorithms and Computations" (Oxford, 2006)
  • M Plischke, B Bergersen, "Equilibrium Statistical Physics" (World Scientific)
  • L. D. Landau, E. M. Lifshitz, "Statistical Physics" (Pergamon)
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