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  • Foundations of Data Science with Python

Online Resources for Book Chapters

  • 1. Introduction
    • 1.1. Who is this book for?
    • 1.2. Why learn data science from this book?
    • 1.3. What is data science?
    • 1.4. What data science topics does this book cover?
    • 1.5. What data science topics does this book not cover?
    • 1.6. Extremely Brief Intro to Jupyter and Python
    • 1.7. Chapter Summary
  • 2. First Simulations, Visualizations, and Statistical Tests
    • 2.1. Motivating Problem: Is This Coin Fair?
    • 2.2. First Computer Simulations
    • 2.3. First Visualizations: Scatter Plots and Histograms
    • 2.4. First Statistical Tests
    • 2.5. Chapter Summary
  • 3. First Visualizations and Statistical Tests with Real Data
    • 3.1. Introduction to Pandas
    • 3.2. Visualizing Multiple Data Sets - Part 1: Scatter Plots
    • 3.3. Partitions
    • 3.4. Summary Statistics
    • 3.5. Visualizing Multiple Data Sets - Part 2: Histograms for Partitioned Data
    • 3.6. Null Hypothesis Testing with Real Data
    • 3.7. A Quick Preview of Two-Dimensional Statistical Methods
    • 3.8. Chapter Summary
  • 4. Introduction to Probability
    • 4.1. Outcomes, Sample Spaces, and Events
    • 4.2. Relative Frequencies and Probabilities
    • 4.3. Fair Experiments
    • 4.4. Axiomatic Probability
    • 4.5. Corollaries to the Axioms of Probability
    • 4.6. Combinatorics
    • 4.7. Chapter Summary
  • 5. Null Hypothesis Tests
    • 5.1. Statistical Studies
    • 5.2. General Resampling Approaches for Null Hypothesis Significance Testing
    • 5.3. Calculating \(p\)-Values
    • 5.4. How to Sample from the Pooled Data
    • 5.5. Example Null Hypothesis Significance Tests
    • 5.6. Bootstrap Distribution and Confidence Intervals
    • 5.7. Types of Errors and Statistical Power
    • 5.8. Summary
  • 6. Dependence and Independence
    • 6.1. Simulating and Counting Conditional Probabilities
    • 6.2. Conditional Probability: Notation and Intuition
    • 6.3. Formally Defining Conditional Probability
    • 6.4. Relating Conditional and Unconditional Probabilities
    • 6.5. More on Simulating Conditional Probabilities
    • 6.6. Statistical Independence
    • 6.7. Conditional Probabilities and Independence in Fair Experiments
    • 6.8. Conditioning and (In)dependence
    • 6.9. Chain Rules and Total Probability
    • 6.10. Summary
  • 7. Introduction to Bayesian Methods
    • 7.1. Bayes’ Rule
    • 7.2. Bayes’ Rule in Systems with Hidden State
    • 7.3. Optimal Decisions for Discrete Stochastic Systems
    • 7.4. Bayesian Hypothesis Testing
    • 7.5. Chapter Summary
  • 8. Random Variables
    • 8.1. Definition of a Real Random Variable
    • 8.2. Discrete Random Variables
    • 8.3. Cumulative Distribution Functions
    • 8.4. Important Discrete RVs
    • 8.5. Continuous Random Variables
    • 8.6. Important Continuous Random Variables
    • 8.7. Histograms of Continuous Random Variables and Kernel Density Estimation
    • 8.8. Conditioning with Random Variables
    • 8.9. Chapter Summary
  • 9. Moments, Parameter Estimation, and Binary Hypothesis Tests on Sample Means
    • 9.1. Expected Value
    • 9.2. Expected Value of a Continuous Random Variable with SymPy
    • 9.3. Moments
    • 9.4. Parameter Estimation
    • 9.5. Confidence Intervals for Estimates
    • 9.6. Testing a Difference of Means
    • 9.7. Sampling and Bootstrap Distributions of Parameters
    • 9.8. Effect Size, Power, and Sample Size Selection
    • 9.9. Summary
  • 10. Decision Making with Observations from Continuous Distributions
    • 10.1. Binary Decisions from Continuous Data: Non-Bayesian Approaches
    • 10.2. Point Conditioning
    • 10.3. Optimal Bayesian Decision Making with Continuous Random Variables
    • 10.4. Summary
  • 11. Categorical Data, Tests for Dependence, and Goodness of Fit for Discrete Distributions
    • 11.1. Tabulating Categorical Data and Creating a Test Statistic
    • 11.2. Null Hypothesis Significance Testing for Dependence in Contingency Tables
    • 11.3. Chi-Square Goodness-of-Fit Test
    • 11.4. Summary
  • 12. Multidimensional Data: Vectors and Linear Regression
    • 12.1. Summary Statistics for Vector Data
    • 12.2. Linear Regression
    • 12.3. Null Hypothesis Tests for Correlation
    • 12.4. Nonlinear Regression Tests
    • 12.5. Summary
  • 13. Working with Dependent Data in Multiple Dimensions
    • 13.1. Jointly Distributed Pairs of Random Variables
    • 13.2. Standardization and Linear Transformation of Numerical Data
    • 13.3. Decorrelating Random Vectors and Multi-Dimensional Data
    • 13.4. Principal Components Analysis
    • 13.5. Summary

Online Resources for Book Chapters

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Index

A | C | D | E | F | H | I | J | M | P | S | U | V

A

  • array
  • axioms of probability
    • corollaries

C

  • cardinality (of a set)
  • complement (\overline{A})
  • countably infinite (set)

D

  • DeMorgan’s Laws
  • Distributive Laws

E

  • effect size
  • element or member (of a set)
  • empty set (\emptyset)

F

  • finite (set)

H

  • hidden state
  • hypothesis testing
    • Bayesian

I

  • intersection (\bigcap)
  • interval (of the real line)

J

  • Jupyter
    • LaTeX

M

  • matrix

P

  • Pandas
  • power set (2^S)

S

  • set
  • set membership (\in)
  • simulation
    • computer
  • subset (\subset)

U

  • uncountably infinite (set)
  • union (\bigcup)

V

  • vector

By John M. Shea

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