Bayesian Spline Estimation of the Varying-coefficient Models

The model being studied in this paper is the varying-coefficient model y=x₁β₁(t)+x₂β₂(t)+…+x_pβ_p(t)+∈, where ∈~N(0,σ²), and β_r(t),r=1,…,P are continuous smooth function. Suppose that the function coefficient βr(t) are the spline functions of degree three and the knot number is given the uniform prior. The coefficient functions are estimated by the method of the Bayesian model averaging. This methods take advantage of the smoothing parameter of each coefficient function being allowed to be different and considering the uncertainty of the knot number.