Bayesian Lasso Models – With Application to Sports Data

Abstract

Several statistical models were proposed by researchers to fulfill the objective of correctly predicting the winners of sports game, for example, the generalized linear model (Magel & Unruh, 2013) and the probability self-consistent model (Shen et al., 2015). This work studied Bayesian Lasso generalized linear models. A hybrid model estimation approach of full and Empirical Bayesian was proposed. A simple and efficient method in the EM step, which does not require sample mean from the random samples, was also introduced. The expectation step was reduced to derive the theoretical expectation directly from the conditional marginal. The findings of this work suggest that future application will significantly cut down the computation load. Due to Lasso (Tibshirani, 1996)’s desired geometric property, the Lasso method provides a sharp power in selecting significant explanatory variables and has become very popular in solving big data problem in the last 20 years. This work was constructed with Lasso structure hence can also be a good fit to achieve dimension reduction. Dimension reduction is necessary when the number of observations is less than the number of parameters or when the design matrix is non-full rank. A simulation study was conducted to test the power of dimension reduction and the accuracy and variation of the estimates. For an application of the Bayesian Lasso Probit Linear Regression to live data, NCAA March Madness (Men’s Basketball Division I) was considered. In the end, the predicting bracket was used to compare with the real tournament result, and the model performance was evaluated by bracket scoring system (Shen et al., 2015).