Fitting a Bayesian Model Based on Markov Chain Monte Carlo

Open Access
Author:
El-Zaatari, Helal Mohamad
Area of Honors:
Mathematics
Degree:
Bachelor of Science
Document Type:
Thesis
Thesis Supervisors:
  • Matthew Logan Reimherr, Thesis Supervisor
  • Sergei Tabachnikov, Honors Advisor
Keywords:
  • Statistics
  • Mathematics
Abstract:
We are currently trying to fit a functional regression model on a collection of functions. How-ever, these functions are very erratically observed and are thus sparse. The approach we used was trying to fit a Bayesian model based on Monte Carlo Markov Chains. Bayesian models are a lot better at handling sparse or missing variable problems such as this one. Specifically for this the-sis, we used the Monte Carlo Markov algorithm called Gibbs Sampling. This method updates its parameters based on the target density. This allows us to break complex problems into a series of easier but interrelated problems. Our goal was to estimate a function f(t)