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所在平台: Coursera |
课程主页: https://www.coursera.org/learn/probability-theory-foundation-for-data-science
课程评论：没有评论
课程总结：概率论：数据科学基础 本课程旨在帮助学员理解概率论的基础及其与统计学和数据科学的关系。课程内容包括概率计算的基本概念、独立和依赖事件、条件事件的定义，以及离散和连续随机变量的学习。此外，课程的最后部分将专注于高斯（正态）随机变量和中心极限定理，以及它们对统计学和数据科学的重要性。 课程大纲如下： 1. **课程介绍**：提供课程的基本信息和学习准备。 2. **描述性统计与概率公理**：理解概率的基础及其在统计学和数据科学中的重要关系，学习如何计算概率、独立和依赖事件，以及条件事件的定义。 3. **条件概率**：引入条件概率的概念及贝叶斯公式，理解独立事件的基本概念。 4. **离散随机变量**：学习不同的命名离散随机变量及其性质，包括期望值和方差的计算。 5. **连续随机变量**：扩展随机变量的定义，重点学习连续随机变量的分析。 6. **联合分布与协方差**：探讨多个随机变量的结果与影响，学习联合分布的概念，将概率理论推广到多元情况。 7. **中心极限定理**：介绍中心极限定理及其在分析数据中的应用，特别是如何表征大数据集的均值分布。 该课程可作为科罗拉多大学博尔德分校数据科学硕士学位（MS-DS）的一部分在Coursera上获得学术学分。MS-DS项目汇集了应用数学、计算机科学、信息科学等多个学科的教师，适合具有计算机科学、信息科学、数学和统计背景的广泛学生群体。如需了解更多关于MS-DS项目的信息，请访问 https://www.coursera.org/degrees/master-of-science-data-science-boulder。
Name:Start Here!
Description:Welcome to the course! This module contains logistical information to get you started!
Name:Descriptive Statistics and the Axioms of Probability
Description:Understand the foundation of probability and its relationship to statistics and data science. We’ll learn what it means to calculate a probability, independent and dependent outcomes, and conditional events. We’ll study discrete and continuous random variables and see how this fits with data collection. We’ll end the course with Gaussian (normal) random variables and the Central Limit Theorem and understand it’s fundamental importance for all of statistics and data science.
Name:Conditional Probability
Description:The notion of “conditional probability” is a very useful concept from Probability Theory and in this module we introduce the idea of “conditioning” and Bayes’ Formula. The fundamental concept of “independent event” then naturally arises from the notion of conditioning. Conditional and independent events are fundamental concepts in understanding statistical results.
Name:Discrete Random Variables
Description:The concept of a “random variable” (r.v.) is fundamental and often used in statistics. In this module we’ll study various named discrete random variables. We’ll learn some of their properties and why they are important. We’ll also calculate the expectation and variance for these random variables.
Name:Continuous Random Variables
Description:In this module, we’ll extend our definition of random variables to include continuous random variables. The concepts in this unit are crucial since a substantial portion of statistics deals with the analysis of continuous random variables. We’ll begin with uniform and exponential random variables and then study Gaussian, or normal, random variables.
Name:Joint Distributions and Covariance
Description:The power of statistics lies in being able to study the outcomes and effects of multiple random variables (i.e. sometimes referred to as “data”). Thus, in this module, we’ll learn about the concept of “joint distribution” which allows us to generalize probability theory to the multivariate case.
Name:The Central Limit Theorem
Description:The Central Limit Theorem (CLT) is a crucial result used in the analysis of data. In this module, we’ll introduce the CLT and it’s applications such as characterizing the distribution of the mean of a large data set. This will set the stage for the next course.
Understand the foundations of probability and its relationship to statistics and data science. We’ll learn what it means to calculate a probability, independent and dependent outcomes, and conditional events. We’ll study discrete and continuous random variables and see how this fits with data collection. We’ll end the course with Gaussian (normal) random variables and the Central Limit Theorem and understand its fundamental importance for all of statistics and data science. 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.
