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

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Probability Elements

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• Kolmogorov fundamentals and formalism

• Discrete distributions

• Probabilistic paradoxes

• Law of large numbers and its implications

• Central limit theorem

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Stochastic processes

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• Discrete Markov chains

• Applications

• Fundamental theorems

• Continuous Markov chains

• Monte Carlo method

• Gibbs sampling

• Metropolis Algorithm

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