Mathematical Sciences: Bayesian Inference for Nonparametric Regression in Generalized Linear Models

小行星9410984 该建议的重点是非高斯响应变量对一组给定预测变量的函数依赖性建模。这方面的示例包括逻辑回归模型（其中响应是二进制的）和对数线性泊松模型（其中响应表示给定时间间隔内的事件计数）。感兴趣的函数估计非参数，使用广义平滑样条。 推理过程的基础上的贝叶斯公式，其中一个随机过程之前施加在这个功能，将进行调查。 一个更完整的答案需要有限的样本计算，这是一个计算强加的任务。将探索用于后验分析的蒙特卡罗方法。 ***

9410984 Raghavan The focus of this proposal is the modeling of the functional dependence of non-Gaussian response variables on a given set of predictors. Examples of this include the logistic regression model, where the response is binary and the log-linear Poisson model where the response represents counts of incidents in a given time interval. The function of interest is estimated nonparametrically, using generalized smoothing splines. Inferential procedures based on a Bayesian formulation, wherein a stochastic process prior is imposed on this function, will be investigated. A more complete answer requires finite sample calculations which is a computationally imposing task. Monte Carlo methods for analysis of the posterior will be explored. ***