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Full-Text Articles in Probability
Comparing North American Professional Sports League Season Formats Using Monte Carlo Simulation, Lathan Gregg
Comparing North American Professional Sports League Season Formats Using Monte Carlo Simulation, Lathan Gregg
Industrial Engineering Undergraduate Honors Theses
Each NFL, NBA, and MLB season consists of a regular season, in which teams play a set number of scheduled games and a playoff, in which qualifying teams compete for a championship. At the conclusion of each season, teams are ranked based on their performance throughout the season. This study aims to investigate the ability of each league's season format to accurately rank teams using Monte Carlo simulation. Matches between two teams are simulated by using the team’s assigned strength ranks to calculate a winning probability for each team. The winning probabilities are simulated with different skill values, dictating how …
Evaluating The Efficiency Of Markov Chain Monte Carlo Algorithms, Thuy Scanlon
Evaluating The Efficiency Of Markov Chain Monte Carlo Algorithms, Thuy Scanlon
Graduate Theses and Dissertations
Markov chain Monte Carlo (MCMC) is a simulation technique that produces a Markov chain designed to converge to a stationary distribution. In Bayesian statistics, MCMC is used to obtain samples from a posterior distribution for inference. To ensure the accuracy of estimates using MCMC samples, the convergence to the stationary distribution of an MCMC algorithm has to be checked. As computation time is a resource, optimizing the efficiency of an MCMC algorithm in terms of effective sample size (ESS) per time unit is an important goal for statisticians. In this paper, we use simulation studies to demonstrate how the Gibbs …