Master's Degree in Stochastics and Data Science

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This is the page about all my works for my master's degree.

Essay: Coupling from the past

Markov chain Monte Carlo methods allow to compute difficult integrals and sample from complex distributions, opening new possibilities. Gibbs sampler gained a lot of popularity, dealing with multidimensional problems. The main issue is to be able to sample directly from the stationary distribution of the Markov chain, that is to get perfect samples. An efficient algorithm to accomplish that is the coupling from the past (CFTP) algorithm. In this essay, we will describe and prove the functionality of CFTP algorithm. Furthermore, a practical application in image restoration is given, applying CFTP to a Gibbs sampler.