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所在平台: Coursera |
课程主页: https://www.coursera.org/learn/statistical-inference-for-estimation-in-data-science
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课程名称：数据科学中的统计推断与估计 课程概述： 本课程介绍了统计推断、抽样分布和置信区间的基本概念。学生将学习如何定义和构建良好的估计量，掌握矩估计法、最大似然估计法，以及如何在更广泛的场合构造置信区间的方法。 该课程可作为科罗拉多大学博尔德分校数据科学硕士（MS-DS）学位的学术学分，由Coursera平台提供。MS-DS是一个跨学科的学位项目，汇集了应用数学、计算机科学、信息科学等多个领域的教师。该项目采取基于表现的招生方式，无需申请流程，适合具有计算机科学、信息科学、数学和统计学等广泛背景和/或职业经验的人士。有关MS-DS项目的更多信息，请访问：https://www.coursera.org/degrees/master-of-science-data-science-boulder。 课程大纲： 1. 开始学习！ 本模块包含启动课程所需的后勤信息。 2. 点估计 在本模块中，您将学习如何仅基于小样本信息估计大总体的参数。将讨论一些有助于区分好估计量与坏估计量的理想属性，回顾期望、方差和协方差的概念，并介绍被称为“矩法”的形式化（同时直观）估计方法。 3. 最大似然估计 本模块将学习似然函数的概念及最大似然估计。我们将为一个和两个参数的例子以及参数函数构建最大似然估计量（MLE），并利用MLE的保持属性。 4. 最大似然估计量的大样本性质 本模块探讨最大似然估计量的大样本性质，包括渐近无偏性和渐近正态性。我们将学习如何计算“Cramér-Rao下界”，这是无偏估计量方差的最小基准。 5. 正态分布的置信区间 在本模块中，我们学习“区间估计”的理论。将了解置信区间的定义和正确解释，并学习基于大样本和小样本为未观察总体的均值构造置信区间，包括已知和未知方差的情况。 6. 超越正态分布：释放置信区间！ 本模块将前四模块的课程内容推广到其他感兴趣的量以及其他分布。将更深入地探讨双样本置信区间以及总体方差和比例的置信区间，同时学习如何为非正态分布中的参数开发置信区间。
Name:Start Here!
Description:Welcome to the course! This module contains logistical information to get you started!
Name:Point Estimation
Description:In this module you will learn how to estimate parameters from a large population based only on information from a small sample. You will learn about desirable properties that can be used to help you to differentiate between good and bad estimators. We will review the concepts of expectation, variance, and covariance, and you will be introduced to a formal, yet intuitive, method of estimation known as the "method of moments".
Name:Maximum Likelihood Estimation
Description: In this module we will learn what a likelihood function is and the concept of maximum likelihood estimation. We will construct maximum likelihood estimators (MLEs) for one and two parameter examples and functions of parameters using the invariance property of MLEs.
Name:Large Sample Properties of Maximum Likelihood Estimators
Description:In this module we will explore large sample properties of maximum likelihood estimators including asymptotic unbiasedness and asymptotic normality. We will learn how to compute the “Cramér–Rao lower bound” which gives us a benchmark for the smallest possible variance for an unbiased estimator.
Name:Confidence Intervals Involving the Normal Distribution
Description: In this module we learn about the theory of “interval estimation”. We will learn the definition and correct interpretation of a confidence interval and how to construct one for the mean of an unseen population based on both large and small samples. We will look at the cases where the variance is known and unknown.
Name:Beyond Normality: Confidence Intervals Unleashed!
Description: In this module, we will generalize the lessons of Module 4 so that we can develop confidence intervals for other quantities of interest beyond the distribution mean and for other distributions entirely. This module covers two sample confidence intervals in more depth, and confidence intervals for population variances and proportions. We will also learn how to develop confidence intervals for parameters of interest in non-normal distributions.
This course introduces statistical inference, sampling distributions, and confidence intervals. Students will learn how to define and construct good estimators, method of moments estimation, maximum likelihood estimation, and methods of constructing confidence intervals that will extend to more general settings. This course can be taken for academic credit as part of CU Boulder’s Master of Science in Data Science (MS-DS) degree offered on the Coursera platform. The MS-DS is an interdisciplinary degree that brings together faculty from CU Boulder’s departments of Applied Mathematics, Computer Science, Information Science, and others. With performance-based admissions and no application process, the MS-DS is ideal for individuals with a broad range of undergraduate education and/or professional experience in computer science, information science, mathematics, and statistics. Learn more about the MS-DS program at https://www.coursera.org/degrees/master-of-science-data-science-boulder. Logo adapted from photo by Christopher Burns on Unsplash.
