A0531
Title: Bayesian simultaneous credible bands for polynomial regression
Authors: Fei Yang - The University of Manchester (United Kingdom) [presenting]
Abstract: A Bayesian method is proposed for constructing simultaneous credible bands (SCBs) for the true regression line in univariate polynomial regression over a finite interval of covariate x. Unlike pointwise intervals, a 1-alpha SCB can provide global coverage of the regression line with the probability of at least 1-alpha. Leveraging a normal-gamma conjugate prior, the posterior distribution is derived from targeted parameters of interest, and a Monte-Carlo-based method is used to compute the critical value required for the band. The Bayesian framework exhibits advantages over the frequentist methods in more robust and stable estimates, especially in cases with limited data. Numerical simulation results show that the proposed method has satisfactory frequentist properties and contains the true regression model with the probability of at least 1-alpha under different settings. Real data analysis in drug stability studies also verifies the effectiveness of the proposed framework.
