Academic project led by Rémi Calvet, Antoine Gilson, Anna Mosaki and Louis Reisse about : Zero variance Markov chain Monte Carlo for Bayesian estimators, and control variates for GARCH model, derived from these two papers : https://doi.org/10.1007/s11222-012-9344-6 and https://doi.org/10.1007/s11222-021-10011-z.
The plan we followed during our project is the following :
I - Presentation of the ZV principle of the article, in a general case II - Implementation of a Random Walk Metropolis Sampler III - Use of Control Variates for Variance Reduction IV - Expansion to Higher Order Polynomials V - Bonus: Linear Regression Validity