统计建模

统计建模（48课时/3学分）

Statistical Modeling (48 hours/3 credits)

课程描述：

  应用统计学家的关键要求之一是能够制定适当的统计模型，然后将其应用于数据以回答感兴趣的问题。大多数情况下，此类模型可被视为将响应变量与一个或多个解释变量相关联。例如，在医学实验中，我们可能会通过将患者结果与接受的治疗联系起来来评估新的治疗方法，同时允许年龄，性别和疾病严重程度等背景变量。在本课程中，对线性模型进行了严格的讨论，并进行扩展。本课程有很强的实用性，统计软件R语言被广泛使用。本课程涵盖的主题包括：线性模型、最小二乘估计、广义最小二乘估计、估计量的性质、高斯-马尔可夫定理;线性模型的子空间公式、正交投影;回归模型、因子实验、方差分析和模型公式;回归诊断、残差、模型诊断、变换、Box-Cox 模型、模型选择和模型构建策略;逻辑回归模型;泊松回归模型。

  One of the key requirements of an applied statistician is the ability to formulate appropriate statistical models and then apply them to data in order to answer the questions of interest. Most often, such models can be seen as relating a response variable to one or more explanatory variables. For example, in a medical experiment we may seek to evaluate a new treatment by relating patient outcome to treatment received while allowing for background variables such as age, sex and disease severity. In this course, a rigorous discussion of the linear model is given and various extensions are developed. There is a strong practical emphasis and the statistical package R is used extensively. Topics covered are: the linear model, least squares estimation, generalized least squares estimation, properties of estimators, the Gauss-Markov theorem; geometry of least squares, subspace formulation of linear models, orthogonal projections; regression models, factorial experiments, analysis of covariance and model formulae; regression diagnostics, residuals, influence diagnostics, transformations, Box-Cox models, model selection and model building strategies; logistic regression models; Poisson regression models.