- Coupling from the Past for Statistical Mechanics Models
- Project Year:
2024
- REU Student (s):
Jasmine Khalil | Pennsylvania State University-Main Campus PA
- Student 1 Institution:
Pennsylvania State University-Main Campus
- Project Mentor:
Pierre Bellec
- Project Mentor Area:
Statistics
- Project Abstract:
Coupling from the past is a variation of traditional Markov Chain Monte Carlo methods and is used to create a perfect simulation of a model. Many MCMC algorithms sample from a close approximation of the stationary distribution. As a result, we end up with undesired convergence issues because we want to sample from the exact distribution. CFTP solves this issue and produces perfect samples from the desired stationary distribution. In this paper, we show how Coupling from the Past differs from ordinary MCMC and optimize it for a perfect simulation of a statistical mechanics model, the Ising model of ferromagnetic materials. We anticipate that our work may be a starting point for the simulation of a broader range of more sophisticated models with real-world applications relating to phase transition phenomena using this perfect sampling.
