Bayesian Bidimensional Regression and Its Extension
Hae-Ri Lee · Open Scholarship Institutional Repository (Washington University in St. Louis) · 2012
Bidimensional regression analysis is used for comparing the similarity between two plane figures (Tobler,1994).The basic bidimensional regression can be written as a linear regression model after re-parameterization and has been traditionally estimated by the ordinary least squares.In this dissertation, we propose a Bayesian approach to bidimensional regression and further consider its extension to a cognitive study that studies the relationship between a real map and memorized maps from many subjects.A hierarchical model is further proposed to incorporate random effects that describe the difference among subjects.Also, we develop a Gibbs sampler for estimating this hierarchical model.The proposed method is then applied to a real cognitive study.