An Evaluation of Stein Thinning for the Post-Processing of Markov Chain Monte Carlo Linear Regression Output
Open Access
- Author:
- Licata, Michael
- Area of Honors:
- Statistics
- Degree:
- Bachelor of Science
- Document Type:
- Thesis
- Thesis Supervisors:
- Stephen Berg, Thesis Supervisor
John Joseph Hannan, Thesis Honors Advisor - Keywords:
- Markov Chain Monte Carlo
Stein Thinning
Zero Variance Control Variates
Linear Regression
Bayesian Statistics
Post Processing - Abstract:
- In recent years many fields of research have turned to Markov Chain Monte Carlo (MCMC) sampling methods in order to better understand populations and systems that have probability distributions that are intractable, or impossible to determine in polynomial time. When using MCMC methods, more complicated systems require larger MCMC Chains to compute accurate estimates, which causes the output to be difficult or impossible to utilize within given CPU constraints. To solve this problem, post-processing methods have been developed to decrease the size of these outputs while not sacrificing their MSE, bias or variance. Chief among these methods are Stein Thinning and Zero Variance Control Variates (ZVCV), which are both evaluated in this paper and are compared with Basic or Vanilla MCMCM chains and a ground truth MCMC sample. It is determined that Stein Thinning has similar variance reduction power as ZVCV while maintaining lower bias and MSE. Stein Thinning’s MSE, bias and variance are also found to be within a factor of 10 when compared to the raw MCMC chain that the Stein Thinned samples are computed from. While these results are promising, Stein Thinning fails to maintain these impressive results when the burn in tail is not removed before thinning the samples. These results, and the methods used to obtain them, are explored in depth and conclusions relevant to the field of Markov Chain Monte Carlo sampling are presented.