AI 中文总结
针对矩约束模型，提出曲率校准准贝叶斯更新方法，经理论证明与模拟验证，可改善协方差校准与区间覆盖率，适用于含被试内依赖的纵向二元响应数据。
AI 中文摘要
当完整似然不可用时，矩约束为拟贝叶斯推断提供了灵活基础，但二次矩准则中的加权矩阵既决定矩的相对重要性，也决定后验更新的信息尺度。我们提出曲率校准准贝叶斯更新，该方法使用在自洽拟后验中心处评估的矩条件的协方差（或长期协方差）的逆。所得的不动点过程在协方差估计和固定加权拟后验的模拟之间交替，从而避免了每次模拟运行期间依赖参数的加权。在有效总体权重下固定加权拟后验的伯恩斯坦-冯·米塞斯条件下，我们证明校准映射是局部压缩的，其不动点以标准参数速率一致，且在依赖校准数据的权重下，高斯近似仍然成立，协方差由逆戈达姆信息矩阵给出。在一致四阶矩条件下，缩放后的拟后验协方差收敛到同一矩阵，因此拟后验与重复抽样不确定性在一阶近似上一致。模拟结果显示，经过几次更新后，协方差校准和区间覆盖率得到改善。对纵向二元响应数据的应用说明了该方法适用于被试内依赖和过度识别残差矩的情形。
英文摘要
Moment restrictions provide a flexible basis for quasi-Bayesian inference when a full likelihood is unavailable, but the weighting matrix in a quadratic moment criterion determines both the relative importance of the moments and the information scale of posterior updating. We propose curvature-calibrated quasi-Bayesian updating, which uses the inverse of the covariance (or long-run covariance) of the moment conditions evaluated at a self-consistent quasi-posterior center. The resulting fixed-point procedure alternates between covariance estimation and simulation from a fixed-weight quasi-posterior, thereby avoiding parameter-dependent weighting during each simulation run. Under a Bernstein-von Mises condition for the fixed-weight quasi-posterior at the efficient population weight, we show that the calibration map is locally contractive, that its fixed point is consistent at the standard parametric rate, and that the Gaussian approximation continues to hold under the calibrated data-dependent weight, with covariance given by the inverse Godambe information matrix. Under a uniform fourth-moment condition, the scaled quasi-posterior covariance converges to the same matrix, so quasi-posterior and repeated-sampling uncertainty agree to first order. Simulations show improved covariance calibration and interval coverage after a few updates. An application to longitudinal binary-response data illustrates the method with within-subject dependence and overidentified residual moments.
