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利用成对 Copula 分解序列依赖的纵向数据建模AI 解读

Copulas have proven to be very successful tools for the flexible modeling of cross-sectional dependence. In this paper we express the dependence structure of continuous-valued time series data using a sequence of bivariate copulas. This corresponds to a type of decomposition recently called a “vine” in the graphical models literature, where each copula is entitled a “pair-copula.” We propose a Bayesian approach for the estimation of this dependence structure for longitudinal…

高维加性模型中半参数函数的贝叶斯识别、选择与估计AI 解读

In this paper we propose an approach to both estimate and select unknown smooth functions in an additive model with potentially many functions. Each function is written as a linear combination of basis terms, with coefficients regularized by a proper linearly constrained Gaussian prior. Given any potentially rank deficient prior precision matrix, we show how to derive linear constraints so that the corresponding effect is identified in the additive model. This allows for the…

空间贝叶斯变量选择及其在功能磁共振成像中的应用AI 解读

We propose a procedure to undertake Bayesian variable selection and model averaging for a series of regressions located on a lattice. For those regressors that are in common in the regressions, we consider using an Ising prior to smooth spatially the indicator variables representing whether or not the variable is zero or nonzero in each regression. This smooths spatially the probabilities that each independent variable is nonzero in each regression and indirectly smooths…

日内电力负荷的贝叶斯建模与预测AI 解读

The advent of wholesale electricity markets has brought renewed focus on intraday electricity load forecasting. This article proposes a multi-equation regression model with a diagonal first-order stationary vector autoregresson (VAR) for modeling and forecasting intraday electricity load. The correlation structure of the disturbances to the VAR and the appropriate subset of regressors are explored using Bayesian model selection methodology. The full spectrum of finite-sample…

纵向数据的简约协方差矩阵估计AI 解读

This article proposes a data-driven method to identify parsimony in the covariance matrix of longitudinal data and to exploit any such parsimony to produce a statistically efficient estimator of the covariance matrix. The approach parameterizes the covariance matrix through the Cholesky decomposition of its inverse. For longitudinal data, this is a one-step-ahead predictive representation, and the Cholesky factor is likely to have off-diagonal elements that are zero or close…

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自相关误差下的加性非参数回归AI 解读

Summary A Bayesian approach is presented for nonparametric estimation of an additive regression model with autocorrelated errors. Each of the potentially non-linear components is modelled as a regression spline using many knots, while the errors are modelled by a high order stationary autoregressive process parameterized in terms of its autocorrelations. The distribution of significant knots and partial autocorrelations is accounted for using subset selection. Our approach…

非参数二元回归的贝叶斯方法AI 解读

This article outlines a general Bayesian approach to estimating a bivariate regression function in a nonparametric manner. It models the function using a bivariate regression spline basis with many terms. Binary indicator variables corresponding to these terms are introduced to explicitly model the uncertainty of whether or not the terms provide a significant contribution to the regression. The regression function is estimated using an estimate of its posterior mean,…

非参数二维回归的贝叶斯方法AI 解读

This article outlines a general Bayesian approach to estimating a bivariate regression function in a nonparametric manner. It models the function using a bivariate regression spline basis with many terms. Binary indicator variables corresponding to these terms are introduced to explicitly model the uncertainty of whether or not the terms provide a significant contribution to the regression. The regression function is estimated using an estimate of its posterior mean,…

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