Probability & Statistics Essentials for Machine Learning
Chapter 1: Probability Foundations Revisited
Review of Sample Spaces and Events
Conditional Probability and Independence
Bayes' Theorem Explained
Introduction to Random Variables
Expected Value and Variance
Applying Probability Concepts in Python
Quiz for Chapter 1
Chapter 2: Common Probability Distributions
Bernoulli and Binomial Distributions
Poisson Distribution
Uniform Distribution
Normal (Gaussian) Distribution
Exponential Distribution
Properties and Use in Data Modeling
Working with Distributions in SciPy
Hands-on Practical: Simulating and Plotting Distributions
Quiz for Chapter 2
Chapter 3: Descriptive Statistics for Datasets
Measures of Central Tendency: Mean, Median, Mode
Measures of Dispersion: Variance, Standard Deviation, Range
Understanding Skewness and Kurtosis
Percentiles and Quartiles
Correlation Analysis
Distinguishing Correlation from Causation
Visualizing Data Summaries
Calculating Descriptive Stats with Pandas
Practice: Summarizing a Dataset
Quiz for Chapter 3
Chapter 4: Inferential Statistics: Sampling and Estimation
Populations and Samples
Overview of Sampling Methods
The Central Limit Theorem
Understanding Point Estimates
Confidence Intervals Explained
Calculating Confidence Intervals for Means
Hands-on Practical: Sampling Simulation and Interval Estimation
Quiz for Chapter 4
Chapter 5: Hypothesis Testing for Model Evaluation
Formulating Null and Alternative Hypotheses
Understanding Type I and Type II Errors
P-values Explained
Introduction to T-tests
Introduction to Chi-Squared Tests
Analysis of Variance (ANOVA) Overview
Performing Hypothesis Tests using Python
Practice: Applying T-tests to Sample Data
Quiz for Chapter 5
Chapter 6: Introduction to Regression Analysis
The Simple Linear Regression Model
Method of Least Squares Estimation
Interpreting Regression Coefficients
Model Evaluation Metrics (R-squared, MSE)
Assumptions of Linear Regression
Overview of Multiple Linear Regression
Building Regression Models with Python
Hands-on Practical: Fitting and Evaluating a Linear Model
Quiz for Chapter 6
Confidence Intervals Explained
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- All of Statistics: A Concise Course in Statistical Inference, Larry Wasserman, 2004 (Springer) DOI: 10.1007/978-0-387-21736-9 - Provides a rigorous yet accessible treatment of statistical inference, including the theoretical underpinnings of confidence intervals.
- Probability and Statistics for Engineering and the Sciences, Jay L. Devore, 2015 (Cengage Learning) - Offers a comprehensive introduction to probability and statistics, with clear explanations and examples of confidence intervals.
- Practical Statistics for Data Scientists: 50 Essential Concepts, Peter Bruce, Andrew Bruce, Peter Gedeck, 2020 (O'Reilly Media) - Connects statistical concepts like confidence intervals to data science and machine learning applications.
- Introduction to Probability and Statistics, Jeremy Orloff and Jonathan Bloom, 2014 MIT OpenCourseWare (MIT OpenCourseWare) - MIT OpenCourseWare material providing a fundamental exposition on probability and statistical inference, including confidence intervals.