Advanced Probability and Statistical Methods

Advanced Probability and Statistical Methods

This course is part of Statistical Methods for Computer Science Specialization

Instructors: Ian McCulloh

Included with

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6 modules

Gain insight into a topic and learn the fundamentals.

Intermediate level

Recommended experience

5 weeks to complete

at 10 hours a week

Flexible schedule

Learn at your own pace

6 modules

Gain insight into a topic and learn the fundamentals.

Intermediate level

Recommended experience

5 weeks to complete

at 10 hours a week

Flexible schedule

Learn at your own pace

What you'll learn

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.

Skills you'll gain

Tools you'll learn

R Programming

Details to know

Shareable certificate

Add to your LinkedIn profile

Assessments

22 assignments

Taught in English

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This course is part of the Statistical Methods for Computer Science Specialization

When you enroll in this course, you'll also be enrolled in this Specialization.

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There are 6 modules in this course

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.

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.

What's included

2 readings1 plugin

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

What's included

9 videos4 readings5 assignments1 ungraded lab

9 videos Total 126 minutes

Overview 14 minutes
Joint Distributions 15 minutes
Joint Probability Space and Joint PMF 24 minutes
Joint Density Function (PDF) 14 minutes
Expected Value and Marginal Distributions 6 minutes
Joint PDF Example Problem 12 minutes
Conditional Joint Probability Distributions 13 minutes
Independence of Joint Random Variables 15 minutes
R Tutorial 15 minutes

4 readings Total 480 minutes

Reading References 120 minutes
Reading References 120 minutes
Reading References 120 minutes
Reading References 120 minutes

5 assignments Total 120 minutes

Joint Distributed Random Variables 15 minutes
Advanced Concepts in Joint Density Functions and Marginal Distributions 15 minutes
Exploring Joint PDFs and Conditional Probability Distributions 15 minutes
Independence of Joint Random Variables and R Implementation 15 minutes
Joint Distributed Random Variables 60 minutes

1 ungraded lab Total 60 minutes

Practice Lab: Exploring Joint PMFs, Density Functions, and Probability Distributions with R 60 minutes

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.

What's included

7 videos3 readings4 assignments1 ungraded lab

7 videos Total 65 minutes

Expected Value & Median 7 minutes
Mean Time to Failure 9 minutes
Linearity of Expectation 9 minutes
Hat Check Problem 7 minutes
Sum of Indicator Variables 7 minutes
Variance 16 minutes
R Tutorial 10 minutes

3 readings Total 540 minutes

Reading References 180 minutes
Reading References 180 minutes
Reading References 180 minutes

4 assignments Total 105 minutes

Understanding Expected Value, Median, and Mean Time to Failure 15 minutes
Linearity of Expectation and the Hat Check Problem 15 minutes
Variance Analysis and Indicator Variables with R Tutorial 15 minutes
Expectation 60 minutes

1 ungraded lab Total 60 minutes

Practice Lab: Exploring Expectations and Ambulance Travel Distance Using R 60 minutes

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.

What's included

9 videos4 readings5 assignments1 ungraded lab

9 videos Total 94 minutes

Rare Events & Markov 8 minutes
Markov Examples 13 minutes
Murphy's Law 7 minutes
Chebyshev Inequality 6 minutes
Central Limit Theorem 10 minutes
Example CLT 9 minutes
Hypothesis Test 15 minutes
Card Trick 12 minutes
R Tutorial 14 minutes

4 readings Total 240 minutes

Reading References 60 minutes
Reading References 60 minutes
Reading References 60 minutes
Reading References 60 minutes

5 assignments Total 120 minutes

Markov Chains, Rare Events, and Murphy's Law 15 minutes
Chebyshev Inequality and the Central Limit Theorem 15 minutes
Central Limit Theorem Examples and Hypothesis Testing 15 minutes
Card Tricks and R Tutorial for Statistical Analysis 15 minutes
Inequalities and Central Limit Theorem 60 minutes

1 ungraded lab Total 60 minutes

Practice Lab: Statistical Distributions and Hypothesis Testing in R 60 minutes

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

What's included

4 videos2 readings3 assignments1 ungraded lab

4 videos Total 98 minutes

Statistical Hypothesis Testing 10 minutes
T-Test 20 minutes
Regression 37 minutes
R Tutorial- Statistical Testing 31 minutes

2 readings Total 120 minutes

Understanding Data and Basis Statistics 60 minutes
Understanding Data and Basis Statistics 60 minutes

3 assignments Total 90 minutes

Statistical Hypothesis Testing and T-Tests 15 minutes
Regression and R Tutorial 15 minutes
Statistical Testing 60 minutes

1 ungraded lab Total 60 minutes

Practice Lab: Simulation of Arbitrary Random Variables and Statistical Analysis in Medical Imaging 60 minutes

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

What's included

8 videos4 readings5 assignments1 ungraded lab

8 videos Total 103 minutes

The Poisson Process 13 minutes
Examples of the Poisson Process 18 minutes
Markov Chains 7 minutes
Markov Chain Example 21 minutes
Limiting Probabilities 8 minutes
R Tutorial 14 minutes
Markov chain using Jupyter Notebook 9 minutes
Applying Markov Chain 14 minutes

4 readings Total 135 minutes

Reading References 40 minutes
Reading References 40 minutes
Reading References 40 minutes
Application of Markov Chains to COVID-19 estimation COVID Bayesian Data August PDF 15 minutes

5 assignments Total 120 minutes

Statistical Hypothesis Testing and T-Tests 15 minutes
Regression and R Tutorial 15 minutes
Limiting Probabilities and R Tutorial 15 minutes
Mastering Markov Chains: From Jupyter Notebook Basics to Real-World Applications 15 minutes
Markov Chain 60 minutes

1 ungraded lab Total 60 minutes

Practice Lab: Markov Analysis in R 60 minutes

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Instructors

Ian McCulloh

Johns Hopkins University

17 Courses 25,157 learners

Tony Johnson

Johns Hopkins University

3 Courses 2,689 learners

Offered by

Johns Hopkins University

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