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Advanced Probability and Statistical Methods

Advanced Probability and Statistical Methods

本课程是 Statistical Methods for Computer Science 专项课程的一部分

位教师：Ian McCulloh

包含在中

了解更多

6个模块

深入了解一个主题并学习基础知识。

中级等级

推荐体验

5 周完成

在 10 小时一周

灵活的计划

自行安排学习进度

6个模块

深入了解一个主题并学习基础知识。

中级等级

推荐体验

5 周完成

在 10 小时一周

灵活的计划

自行安排学习进度

您将学到什么

Learn to analyze relationships between random variables through joint probability distributions and independence concepts.
Understand how to calculate and interpret expected values, variances, and correlations for random variables.
Acquire essential skills in conducting statistical tests, including T-tests and confidence intervals, for data analysis.
Explore the principles of Markov chains and their applications in modeling systems with memoryless properties and calculating entropy.

您将获得的技能

您将学习的工具

要了解的详细信息

可分享的证书

添加到您的领英档案

作业

22 项作业

授课语言：英语（English）

91%

of learners achieved a positive career outcome

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积累特定领域的专业知识

本课程是 Statistical Methods for Computer Science 专项课程专项课程的一部分

在注册此课程时，您还会同时注册此专项课程。

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获得对主题或工具的基础理解
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该课程共有6个模块

The course "Advanced Probability and Statistical Methods" provides a deep dive into advanced probability and statistical methods, essential for mastering data analysis in computer science. Covering joint distributions, expectation, statistical testing, and Markov chains, you'll explore key concepts and techniques that underpin modern data-driven decision-making. By engaging with real-world problems, you’ll learn to apply these methods effectively, gaining insights into the relationships between random variables and their applications in diverse fields.

Completing this course equips you with the skills to analyze complex data sets and make informed predictions, enhancing your proficiency in statistical reasoning and inference. Unique to this course is its blend of theoretical foundations and practical applications, ensuring that you can not only understand the principles but also implement them using tools like R. Whether you're pursuing a career in data science, machine learning, or any data-centric discipline, this course will empower you to tackle challenging statistical problems and drive meaningful insights from data.

单元详情

This course provides a comprehensive overview of probability theory and statistical inference, covering joint probability distributions, independence, and conditional distributions. Students will explore expected values, variances, and key statistical theorems, including the central limit theorem. Hypothesis testing, regression analysis, and stochastic processes such as Poisson processes and Markov chains will also be examined. Through practical applications and problem-solving, participants will gain essential skills in data analysis and interpretation.

涵盖的内容

2篇阅读材料1个插件

This module presents the joint distributions of multiple random variables, both discrete and continuous and introduces the concept of independence.

涵盖的内容

9个视频4篇阅读材料5个作业1个非评分实验室

9个视频总计126分钟

Overview14分钟
Joint Distributions15分钟
Joint Probability Space and Joint PMF24分钟
Joint Density Function (PDF)14分钟
Expected Value and Marginal Distributions6分钟
Joint PDF Example Problem12分钟
Conditional Joint Probability Distributions13分钟
Independence of Joint Random Variables15分钟
R Tutorial15分钟

4篇阅读材料总计480分钟

Reading References120分钟
Reading References120分钟
Reading References120分钟
Reading References120分钟

5个作业总计120分钟

Joint Distributed Random Variables15分钟
Advanced Concepts in Joint Density Functions and Marginal Distributions15分钟
Exploring Joint PDFs and Conditional Probability Distributions15分钟
Independence of Joint Random Variables and R Implementation15分钟
Joint Distributed Random Variables60分钟

1个非评分实验室总计60分钟

Practice Lab: Exploring Joint PMFs, Density Functions, and Probability Distributions with R60分钟

This module focuses on the expectation of a random variable and joint random variable. Students will solve problems using the linearity of expectation and identify when its application is inappropriate. We will also explore variance, covariance, and correlation.

涵盖的内容

7个视频3篇阅读材料4个作业1个非评分实验室

7个视频总计65分钟

Expected Value & Median7分钟
Mean Time to Failure9分钟
Linearity of Expectation9分钟
Hat Check Problem7分钟
Sum of Indicator Variables7分钟
Variance16分钟
R Tutorial10分钟

3篇阅读材料总计540分钟

Reading References180分钟
Reading References180分钟
Reading References180分钟

4个作业总计105分钟

Understanding Expected Value, Median, and Mean Time to Failure15分钟
Linearity of Expectation and the Hat Check Problem15分钟
Variance Analysis and Indicator Variables with R Tutorial15分钟
Expectation60分钟

1个非评分实验室总计60分钟

Practice Lab: Exploring Expectations and Ambulance Travel Distance Using R60分钟

This module will apply several limit theorems to solve problems to include the central limit theorem, the Markov inequality, and the Chebyshev inequality. We will also prove Murphy’s Law.

涵盖的内容

9个视频4篇阅读材料5个作业1个非评分实验室

9个视频总计94分钟

Rare Events & Markov8分钟
Markov Examples13分钟
Murphy's Law7分钟
Chebyshev Inequality6分钟
Central Limit Theorem10分钟
Example CLT9分钟
Hypothesis Test15分钟
Card Trick12分钟
R Tutorial 14分钟

4篇阅读材料总计240分钟

Reading References60分钟
Reading References60分钟
Reading References60分钟
Reading References60分钟

5个作业总计120分钟

Markov Chains, Rare Events, and Murphy's Law15分钟
Chebyshev Inequality and the Central Limit Theorem15分钟
Central Limit Theorem Examples and Hypothesis Testing15分钟
Card Tricks and R Tutorial for Statistical Analysis15分钟
Inequalities and Central Limit Theorem60分钟

1个非评分实验室总计60分钟

Practice Lab: Statistical Distributions and Hypothesis Testing in R60分钟

This module develops student proficiency in probabilistic models to include Markov chains. Students will be introduced to problems involving surprise, uncertainty, and entropy.

涵盖的内容

4个视频2篇阅读材料3个作业1个非评分实验室

4个视频总计98分钟

Statistical Hypothesis Testing10分钟
T-Test20分钟
Regression37分钟
R Tutorial- Statistical Testing31分钟

2篇阅读材料总计120分钟

Understanding Data and Basis Statistics60分钟
Understanding Data and Basis Statistics60分钟

3个作业总计90分钟

Statistical Hypothesis Testing and T-Tests15分钟
Regression and R Tutorial15分钟
Statistical Testing60分钟

1个非评分实验室总计60分钟

Practice Lab: Simulation of Arbitrary Random Variables and Statistical Analysis in Medical Imaging60分钟

This module develops student proficiency in probabilistic models to include Markov chains. Students will be introduced to problems involving surprise, uncertainty, and entropy.

涵盖的内容

8个视频4篇阅读材料5个作业1个非评分实验室

8个视频总计103分钟

The Poisson Process13分钟
Examples of the Poisson Process18分钟
Markov Chains7分钟
Markov Chain Example21分钟
Limiting Probabilities8分钟
R Tutorial14分钟
Markov chain using Jupyter Notebook9分钟
Applying Markov Chain14分钟

4篇阅读材料总计135分钟

Reading References40分钟
Reading References40分钟
Reading References40分钟
Application of Markov Chains to COVID-19 estimation COVID Bayesian Data August PDF15分钟

5个作业总计120分钟

Statistical Hypothesis Testing and T-Tests15分钟
Regression and R Tutorial15分钟
Limiting Probabilities and R Tutorial15分钟
Mastering Markov Chains: From Jupyter Notebook Basics to Real-World Applications15分钟
Markov Chain60分钟