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/1/1d/TD02_ICFP_2016.pdf Tutorial 02: Maximum likelihood, Bootstrap and Bayes without a computer] | + | * [http://www.lps.ens.fr/~krauth/images/1/1d/TD02_ICFP_2016.pdf Tutorial 02: Maximum likelihood, Bootstrap and Bayes without a computer] |
- | ** [http://www.lps.ens.fr/~krauth/images/9/9a/HW02_ICFP_2016.pdf Homework 02: From Maximum Likelihood to Bayes statistics] Useful program: | + | * [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]] | ||
Revision as of 16:56, 15 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
Contents |
Week 1 (7 September 2016): Probability theory
- Tutorial 01: Characteristic functions / Stable distributions
- Homework 01: Chebychev inequality / Rényi formula / Lévy distribution Useful programs:
Week 2 (14 September 2016): Statistical inference
- Tutorial 02: Maximum likelihood, Bootstrap and Bayes without a computer
- Homework 02: From Maximum Likelihood to Bayes statistics Useful program:
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. 10, 340, 1982.
- B. Efron, "Bootstrap methods: another look at the jackknife" The Annals of Statistics, 1-26, 1979.
- P. Diaconis and B. Efron, "Computer intensive methods in statistics" Scientific American 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)