Abstract
In the last fifty years, considerable efforts have been made into the development of ridge regression model, which employs a symmetric penalty function about 0, continuous and non-decreasing in (0, ∞). The reciprocal ridge regression model is an extension of the ridge regression, which employs a decreasing penalty function that is continuous at 0 and converges to infinity when the regression coefficients become closer to zero in the interval (0, ∞). It is well known that the ridge regression is a special case from bridge regression (Frank and Friedman, 1993), whereas the reciprocal ridge regression is a special case from reciprocal bridge regression (Song and Liang, 2015). The objective of this thesis is to examine if the Bayesian reciprocal ridge regression can provide better performance in prediction than Bayesian ridge regression when handling multicollinearity and highdimensional problems. Simulation results and a popular air pollution data analyses show that both approaches have good mixing properties and perform comparably to each to other in terms of prediction accuracy.
