Stochastic Simulation: Metropolis-Hastings Algorithm

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Page 3 of 4

Covers conditional expectation, convergence of random variables, and the strong law of large numbers.

Covers continuous functions with compact support, density, and approximation, focusing on the heat equation.

Covers Markov chains and their applications in algorithms, focusing on Markov Chain Monte Carlo sampling and the Metropolis-Hastings algorithm.

Introduces Dijkstra's algorithm and probabilistic analysis through the Hiring Problem.

Explores Markov chain convergence, emphasizing invariant distribution, Law of Large Numbers, and mean rewards computation.

Introduces the Boltzmann Machine, covering expectation consistency, data clustering, and probability distribution functions.

Covers implicit schemes in numerical analysis for solving partial differential equations.

Covers the limited development of integration and methods for calculating the limit development of functions and antiderivatives.

Covers stability in optimal transport and provides examples of discontinuous optimal solutions.

Covers characteristic functions for random variables and their properties, including independence and convergence.