introduction

Captain Fox sits hunched over the sheet of gridded paper between his feet. Miscallanea glassware positioned on each corner do their best to stop the paper flitting from the draft egressing beneath the canvas walls of the hospital tent. Fox stares intently and curiously down while with his one good hand he blindly picks another match stick from the disorder pile to his side, raises it poingantly above the centre of the grid and releases his hold. The light wood is picked up by a particularly fearsome gust and pushed from its natural downwards fall, landing on the far western edge of the grid. Will this affect the measurement, he wonders?

With the proliferation of models adopting this approach, it seems a modern attempt at an all-encompassing definition of Monte Carlo methods may simply be an approach that employs (pseudo-)random numbers.

In this post, to emphasis the diversity of use-cases, and the necessity of such a broad definition, I outline two very different applications of the Monte Carlo method, specifically it’s use in Geometrical Probability and Markov Chain Monte Carlo methods.