Bayes Penalized Estimation And RJMCMC Sampling For B-Splines Non-parameter Regression Model

B-Splines non-parameter regression model is constructed according to relevant prop-erties and Geometry Algorithms of B-Splines. Among that the knots and degree are s-elected by Reversible jump Markov chain Monte Carlo sampler, splines coefficient is estimated by L2 Difference Penalties with knots information. Concrete content shows as follow:Firstly, express non-parametric model in splines space with parameterization form, B-Splines non-parametric regression model is obtained. Combining the properties of B-Splines basis functions, full column rank condition of basis functions matrix is researched. In that case, redundant information will not be caused by the change of basis functions in the process of reversible jump, so that reasonable constraint for part of parameters is realized.Secondly, based on information criterion method, we construct a priori that meets maximum entropy principle, contains robustness and penalty for inner knots amount and curve degree, so that the model is identifiable and can remove all the redundant infor-mation. Simultaneously, transformation form of knots position and subinterval length is constructed and its concrete form of probability density function is educed. With the derivative recurrence formula of B-Splines curve, L2 difference penalty priori of coeffi-cient vector with knots information weighted is educed, as well as specific cases of differ-ent degree condition are discussed. This form is a generalize form of Bayesian B-Splines under the condition of variable dimension.Thirdly, reversible jump sampler form of B-Splines geometry algorithms is put for-ward. This paper proposes interpretable and separable condition for variable dimension sampler course, thereby the penalty role of posterior distribution in different models is still guaranteed. Meanwhile, the selection processes of curve shape and splines space are separated. Based on above-mentioned condition, reversible transformation forms in the change processes of inner knots and degree are constructed. Analytic expression of Jaco-bian factors is obtained as well as the distribution form of auxiliary random variable that meets the condition.Last, according to simulation research and real data, this method is proved to be effective.