A0908
Title: Bayesian fused lasso and Bayesian HORSES via horseshoe prior
Authors: Yuko Kakikawa - The University of Electro-Communications (Japan) [presenting]
Kaito Shimamura - The University of Electro-Communications (Japan)
Shuichi Kawano - The University of Electro-Communications (Japan)
Abstract: Bayesian fused lasso is one of the Bayesian methods to estimate regression coefficients of a linear regression model. It shrinks both regression coefficients and their successive differences simultaneously by assuming Laplace distributions on both of them. It enables the estimation of regression coefficients with the successive ones fused. However, Bayesian fused lasso tends to over-shrink regression coefficients and their successive differences which are not supposed to be near zero. To overcome this problem, we assume a horseshoe prior on the difference of successive regression coefficients and construct the Bayesian fused lasso modeling. Because horseshoe prior has an infinite spike at zero and a Cauchy-like tail, the proposed method enables us to prevent over-shrinkage of those differences. We also propose a Bayesian hexagonal operator for regression with shrinkage and equality selection (HORSES) with horseshoe prior, which imposes priors on every pair of differences of regression coefficients. To obtain the estimates of the parameters, we develop a Gibbs sampler by using a hierarchical expression of a Laplace prior and a horseshoe prior. Monte Carlo simulations and an application to real data are conducted to investigate the effectiveness of the proposed method.
