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Sampling methods

This course is devoted to the study of various important consequences of the fundamental theorems of probability using so-called sampling methods.

Syllabus

Probability Elements

  • Kolmogorov fundamentals and formalism

  • Discrete distributions

  • Probabilistic paradoxes

  • Law of large numbers and its implications

  • Central limit theorem

 

Stochastic processes

  • Discrete Markov chains

  • Applications

  • Fundamental theorems

  • Continuous Markov chains

  • Monte Carlo method

  • Gibbs sampling

  • Metropolis Algorithm