A Poisson Process Model for Monte Carlo

Gergely Flamich

15/11/2023

gergely-flamich.github.io/talks

1. Poisson processes

• what defines a PP? independence, and mean measure
• simulation:
  1. count first, points second
  2. in time order
• thinning, mapping and restriction: maybe draw a triangle?
• superposition theorem
• equivalence with Gumbel processes in log-space
• emphasize dual view: all the points are there already, vs computational simulation
• the intensity transform for Poisson processes: processes of Poisson type
• Indexing processes
• I won't be dealin with:
  1. Markov Chains
  2. fitting the mean measure of Poisson processes

2. References

• John F. C. Kingman. Poisson Processes. Oxford Studies in Probability. Clarendon Press, 1992. ISBN
• Chris J. Maddison. A Poisson process model for Monte Carlo. Perturbation, Optimization, and

Statistics, pp. 193–232, 2016.

• Chris J. Maddison, Daniel Tarlow, and Tom Minka. A* sampling. In Advances in Neural Information

Processing Systems, volume 27, pp. 3086–3094, 2014.

• Lucas Theis and Noureldin Yosri. Algorithms for the communication of samples. In International

Conference on Machine Learning, 2022.

• Gergely Flamich, Stratis Markou, and José Miguel Hernández Lobato. Fast relative entropy coding

with A* coding. In International Conference on Machine Learning, pp. 6548–6577, 2022.