APM_51056_EP · Engineering Cycle, Year 3 · 2026–27
Monte Carlo Methods
Weekly practical sessions (TP) with notebooks and corrections. Each archive contains the notebook, the compiled PDF of the correction and any code or data it needs.
Practical sessions
Sampling from a Poisson distribution
Direct inversion (Knuth's method) and accept–reject with a logistic envelope; comparison with the theoretical bound.
M/M/1 and M/M/c queues; variance reduction
Simulation of queues (exponential inter-arrivals, Lindley recursion, stationary regime), then control variates, antithetic variables and stratification. The archive also contains TP2 bis: Monte Carlo in the latent space of a variational autoencoder.
Quasi-Monte Carlo and Bayesian inference
Discrepancies, van der Corput and Halton sequences, Koksma–Hlawka; Beta–Binomial inference (MAP, posterior mean, Bayes factors) and the lighthouse problem with a Cauchy likelihood.
Inhomogeneous Poisson process and Brownian bridge
Simulation by thinning and by a Brownian bridge construction.
Gibbs sampling: a Poisson–Gamma change-point model
Gibbs sampler for a rate-change model, applied to mining accident counts.
Metropolis–Hastings
Random-walk and independent proposals, in dimension 1 and dimension 40; the effect of the dimension on acceptance and mixing.
Practical session 7
Coming soon.
Practical session 8
Coming soon.