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所在平台: Coursera |
课程主页: https://www.coursera.org/learn/chances-probability-uncertainty-statistics
课程评论：没有评论
课程名称：机会有多大？统计中的概率与不确定性 课程概述：本课程重点讲解分析师如何测量和描述他们对研究结果的信心。课程开始于关键概率规则和不确定性测量的基本概念，然后应用这些理论于变量及其相关的概率分布。课程的后半部分深入探讨不确定性的计算和解释，包括如何使用检验统计量和置信区间进行假设检验。最后，我们还将讨论假设检验在回归分析中的作用，了解统计显著性系数提供的信息和限制。课程结束时，学员应能够用概率术语讨论统计发现，并解释特定估计的不确定性。 课程大纲： 1. **概率论** 描述：蒙提霍尔问题是一个经典的脑筋急转弯，突显了概率的反直觉特性。示例：选手在游戏节目中从三扇门中选择一扇，其中一扇门后面有车，其他两扇门后面是山羊。选手选定一扇门后，主持人打开一扇有山羊的门，并让选手选择是坚持原选择还是换到另一扇闭门。根据概率，选手应该始终选择换门，这样赢得汽车的概率为2/3，而坚持原选择的概率只有1/3。 2. **随机变量与分布** 描述：本模块探讨您在成年生活中可能常遇但从未以统计角度深入研究的正规分布。我们将讨论概率分布的关键特征及其对量化不确定性的相关性。尽管研究概率论有时感觉远离应用统计，但建立概率的基础理解有助于批判性评估统计模型，尤其是在政策制定者需以统计发现为依据进行决策时。 3. **置信区间与假设检验** 描述：本模块将应用概率、随机变量和分布的概念来衡量和解释不确定性，重点关注统计显著性。我们将通过独立变量（例如针对负面竞选广告的曝光）和依赖变量（投票可能性）关系的检验来确定关系是否显著。 4. **回归分析与民调中的不确定性量化** 描述：在课程的最后一部分，我们将介绍如何衡量回归估计和民调结果的不确定性。我们将讨论当回归模型显示非零关系时，如何判断该关系是否足够不同于零以达到统计显著性，并探讨仅依赖统计显著性做出数据驱动决策的缺陷。 通过本课程，学员能够更好地理解和应用概率及统计概念，评估不确定性和统计显著性，为数据驱动的决策提供理论支持。
Name:Probability Theory
Description:The Monty Hall problem is a classic brain teaser that highlights the often counterintuitive nature of probability. The problem is typically stated as follows: Suppose you're a contestant on a game show and asked to select one of three doors for your prize. Behind one door is a car and behind the other two doors are goats. You pick one door. The host, who knows what's behind each door, opens another, which has a goat. He then gives you the option to stick with your selected door or switch to the other closed door. What should you do? The answer is that, under these circumstances, you should always switch. There is a 2/3 chance of winning the car if you switch and a 1/3 chance of winning if you stick with your original selection. Most people, however, assume that there is only a 50/50 chance of winning if you switch. Hopefully this brain teaser, and content we cover in this module, will help you better approach probabilistic problems.
Name:Random Variables and Distributions
Description:In this module, we'll dive into a topic you've likely encountered all of your adult life but perhaps have never explored from a statistical perspective: the normal curve. More generally, we'll discuss probability distributions, including their key features and relevance to quantifying uncertainty. Although studying probability theory can sometimes feel detached from applied statistics, it's valuable to develop a foundational understanding of probability to be able to critically evaluate statistical models. An appreciation for probability, and its counter-intuitive nature, will help you interpret the uncertainty of a statistical result as accurately as possible. This is particularly important when the stakes are high and policy makers want to know whether or not to act based on a statistical finding.
Name:Confidence Intervals and Hypothesis Testing
Description:In this module we will apply the concepts of probability, random variables and distributions to measuring and interpreting uncertainty. In particular, we'll focus on statistical significance. A relationship is statistically significant if it can be distinguished from zero. Suppose you want to examine the effect of exposure to negative campaign ads on one's likelihood of voting. The independent variable is one's exposure to negative campaign ads and the dependent variable is one's likelihood of voting. If we find that exposure to negative campaign ads has no relationship with the likelihood of voting, we would say that this is a statistically insignificant relationship. If, instead, we find that exposure to negative campaign ads leads to a decline in one's likelihood of voting, we have uncovered a statistically significant (i.e., non-zero) relationship.
Name:Quantifying Uncertainty in Regression Analysis and Polling
Description:In this final module of the course, we'll cover how to measure the uncertainty of regression estimates and poll results. It is often the case that a regression model will reveal a non-zero relationship, but it's important to determine whether that relationship sufficiently different from zero such that we can conclude that the relationship is statistically significant. For example, suppose a regression model reveals that a drug improves patient outcomes by 3.2%. Is 3.2% statistically different from 0? A statistical significance test will answer this question. This module, however, will also discuss some of the drawbacks of relying a statistical significance for data-driven decision making. While statistical significance is an important consideration, it is not the only criterion one should use when determining whether to act on a set of a statistical findings.
This course focuses on how analysts can measure and describe the confidence they have in their findings. The course begins with an overview of the key probability rules and concepts that govern the calculation of uncertainty measures. We’ll then apply these ideas to variables (which are the building blocks of statistics) and their associated probability distributions. The second half of the course will delve into the computation and interpretation of uncertainty. We’ll discuss how to conduct a hypothesis test using both test statistics and confidence intervals. Finally, we’ll consider the role of hypothesis testing in a regression context, including what we can and cannot learn from the statistical significance of a coefficient. By the end of the course, you should be able to discuss statistical findings in probabilistic terms and interpret the uncertainty of a particular estimate.
