Variational inference for varying-coefficient model

In this paper, we propose a variational Bayesian method for estimation of varying-coefficient model. Within the local likelihood framework, we develop variational updates for the approximated posterior and obtain variational lower bound. Mean-field assumption naturally simplifies the estimation procedure, and overcomes the computational burden of traditional Bayesian methods in nonparametric setting. We also propose a Metropolis-Hastings algorithm to select the bandwidth. We conduct simulation study to demonstrate proposed procedure, and apply the proposed estimation method in the analysis of stock return data.