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Monte_Carlo

Various simple and straightforward experiments with the Metropolis-Hastings algorithm and ordinary Monte Carlo methods. Some highlights:

  • The performance of Metropolis-Hastings algorithm is compared to the inverse transform method and to SciPy's library implementation of the multivariate normal distribution.

  • If X and Y are two independent exponentially distributed random variables with parameter 1, then X / (X Y) is uniformly distributed over the open interval (0,1). This analytically derived result is confirmed via Monte Carlo simulation.

  • An extremely simple example of Monte Carlo integration with added comparison of execution time differences between programming in basic style Python versus NumPy style Python.