The following are the written responses to each part of this Monte Carlo simulations project, submitted in completion of the Monte Carlo Simulations (L7) (865G1) module.

Part 1 involved pseudorandom number generation, assessing the generated sample fit to the theoretical distribution and comparing simple sampling to the importance sampling method in determining the expectation value of the distribution, and its associated uncertainty.

Part 2 focused on Markov chain Monte Carlo (MCMC). After explaining some of the theoretical justification for the MCMC method, I computed the empirical invariant distribution of a randomly-generated Markov chain and showed how it almost surely converges to the chain’s theoretical invariant distribution.

Lastly, part 3 involved explaining a particular application of Monte Carlo methods in 1 of 4 published academic articles and attempting to reproduce part of their simulation. I decided to focus on an article which developed a novel agent-based predictive model for the spread of Covid-19 in Israel, utilising pseudo-randomness to simulate real-world phenomena such as proximity between individuals in a geographic region, or probability of infection given vaccination status.