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L1-norm regularized logistic regression models are widely used for analyzing
data with binary response. In those analyses, fusing regression coefficients is
useful for detecting groups of variables. This paper proposes a binomial
logistic regression model with Bayesian fused lasso. Assuming a Laplace prior
on regression coefficients and differences between adjacent regression
coefficients enables us to perform variable selection and variable fusion
simultaneously in the Bayesian framework. We also propose assuming a horseshoe
prior on the differences to improve the flexibility of variable fusion. The
Gibbs sampler is derived to estimate the parameters by a hierarchical
expression of priors and a data-augmentation method. Using simulation studies
and real data analysis, we compare the proposed methods with the existing
method.
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