Bayesian Inference for Regression Copulas
提出一种基于连接函数分解的半参数分布回归平滑器，结合哈密顿蒙特卡洛和变分贝叶斯估计，用于预测电力现货价格分布，比基准模型更准确。
We propose a new semi-parametric distributional regression smoother that is\nbased on a copula decomposition of the joint distribution of the vector of\nresponse values. The copula is high-dimensional and constructed by inversion of\na pseudo regression, where the conditional mean and variance are\nsemi-parametric functions of covariates modeled using regularized basis\nfunctions. By integrating out the basis coefficients, an implicit copula\nprocess on the covariate space is obtained, which we call a `regression\ncopula'. We combine this with a non-parametric margin to define a copula model,\nwhere the entire distribution - including the mean and variance - of the\nresponse is a smooth semi-parametric function of the covariates. The copula is\nestimated using both Hamiltonian Monte Carlo and variational Bayes; the latter\nof which is scalable to high dimensions. Using real data examples and a\nsimulation study we illustrate the efficacy of these estimators and the copula\nmodel. In a substantive example, we estimate the distribution of half-hourly\nelectricity spot prices as a function of demand and two time covariates using\nradial bases and horseshoe regularization. The copula model produces\ndistributional estimates that are locally adaptive with respect to the\ncovariates, and predictions that are more accurate than those from benchmark\nmodels.\n