Abstract

Bayesian regression models have been widely studied and adopted in the statistical literature. Many studies consider the development of reliable priors to select the relevant variables and derive accurate posterior predictive distributions. Moreover in the context of small high-dimensional data, where the number of observations is very small with respect to the number of predictors, sparsity is assumed and many parameters can be set to values close to zero without affecting the fit of the model. Aim of this work is to develop a comparative analysis to empirically evaluate the performances of several Bayesian regression approaches in these contexts. In this study we assume that the predictors can be expressed only as binary variables coding the presence or the absence of a particular characteristic of the system. This binary structure is often present in many real studies, in particular in laboratory experimentation and in very high-dimension genome wide association studies.

摘要

贝叶斯回归模型已在统计文献中得到广泛研究和采用。许多研究考虑开发可靠的先验来选择相关变量并得出准确的后验预测分布。此外，在小的高维数据的情况下，观察值的数量相对于预测变量的数量非常小，假设稀疏性并且可以将许多参数设置为接近零的值而不影响模型的拟合。这项工作的目的是进行比较分析，以凭经验评估几种贝叶斯回归方法在这些情况下的性能。在这项研究中，我们假设预测变量只能表示为编码系统特定特征存在或不存在的二进制变量。