The Metropolis-Hastings Method
R.N. Gangapersad (TU Delft - Electrical Engineering, Mathematics and Computer Science)
H.N. Kekkonen – Mentor (TU Delft - Statistics)
L.E. Meester – Mentor (TU Delft - Applied Probability)
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Abstract
In this report, our goal is to find a way to get some information such as the mean out of high dimensional densities. If we want to calculate the mean we need to calculate integrals, which are difficult to do for high dimensional densities. We cannot use the analytical or classical (deterministic) numerical rules for high dimensional problems for which we want to calculate the mean. These methods take a lot of computational time. To solve this problem we introduced the Markov Chain Monte Carlo (MCMC) method, the method samples from the distribution, and with these samples, we can approximate the mean. Then we explain the theory behind these methods and how we can use it. Then we introduced one MCMC method, in particular, the Metropolis-Hastings Algorithm. We explain how this method works and the theory behind it. From this, we see that the method is very easy to implement and can be used to approximate the mean. Then we approximate the mean for some examples using this method.