Foundations of Data Science with Python

Cover....1 Half Title....2 Series Page....3 Title Page....4 Copyright Page....5 Dedication....6 Contents....8 Acknowledgments....12 Preface....14 1. Introduction....16 1.1. Who is this book for?....16 1.2. Why learn data science from this book?....16 1.3. What is data science?....17 1.4. What data science topics does this book cover?....20 1.5. What data science topics does this book not cover?....21 1.6. Extremely Brief Introduction to Jupyter and Python....21 1.7. Chapter Summary....31 2. First Simulations, Visualizations, and Statistical Tests....32 2.1. Motivating Problem: Is This Coin Fair?....32 2.2. First Computer Simulations....33 2.3. First Visualizations: Scatter Plots and Histograms....35 2.4. First Statistical Tests....42 2.5. Chapter Summary....46 3. First Visualizations and Statistical Tests with Real Data....48 3.1. Introduction to Pandas....49 3.2. Visualizing Multiple Data Sets – Part 1: Scatter Plots....54 3.3. Partitions....62 3.4. Summary Statistics....63 3.5. Visualizing Multiple Data Sets – Part 2: Histograms for Partitioned Data....71 3.6. Null Hypothesis Testing with Real Data....76 3.7. A Quick Preview of Two-Dimensional Statistical Methods....88 3.8. Chapter Summary....91 4. Introduction to Probability....92 4.1. Outcomes, Sample Spaces, and Events....92 4.2. Relative Frequencies and Probabilities....93 4.3. Fair Experiments....98 4.4. Axiomatic Probability....101 4.5. Corollaries to the Axioms of Probability....109 4.6. Combinatorics....114 4.7. Chapter Summary....127 5. Null Hypothesis Tests....128 5.1. Statistical Studies....128 5.2. General Resampling Approaches for Null Hypothesis Significance Testing....135 5.3. Calculating p-Values....142 5.4. How to Sample from the Pooled Data....147 5.5. Example Null Hypothesis Significance Tests....153 5.6. Bootstrap Distribution and Confidence Intervals....156 5.7. Types of Errors and Statistical Power....162 5.8. Chapter Summary....165 6. Conditional Probability, Dependence, and Independence....166 6.1. Simulating and Counting Conditional Probabilities....167 6.2. Conditional Probability: Notation and Intuition....172 6.3. Formally Defining Conditional Probability....174 6.4. Relating Conditional and Unconditional Probabilities....177 6.5. More on Simulating Conditional Probabilities....179 6.6. Statistical Independence....181 6.7. Conditional Probabilities and Independence in Fair Experiments....187 6.8. Conditioning and (In)dependence....191 6.9. Chain Rules and Total Probability....193 6.10. Chapter Summary....201 7. Introduction to Bayesian Methods....202 7.1. Bayes’ Rule....202 7.2. Bayes’ Rule in Systems with Hidden State....210 7.3. Optimal Decisions for Discrete Stochastic Systems....212 7.4. Bayesian Hypothesis Testing....221 7.5. Chapter Summary....230 8. Random Variables....232 8.1. Definition of a Real Random Variable....232 8.2. Discrete Random Variables....244 8.3. Cumulative Distribution Functions....252 8.4. Important Discrete RVs....262 8.5. Continuous Random Variables....280 8.6. Important Continuous Random Variables....294 8.7. Histograms of Continuous Random Variables and Kernel Density Estimation....314 8.8. Conditioning with Random Variables....316 8.9. Chapter Summary....320 9. Expected Value, Parameter Estimation, and Hypothesis Tests on Sample Means....321 9.1. Expected Value....321 9.2. Expected Value of a Continuous Random Variable with SymPy....327 9.3. Moments....330 9.4. Parameter Estimation....341 9.5. Confidence Intervals for Estimates....348 9.6. Testing a Difference of Means....357 9.7. Sampling and Bootstrap Distributions of Parameters....371 9.8. Effect Size, Power, and Sample Size Selection....375 9.9. Chapter Summary....377 10. Decision-Making with Observations from Continuous Distributions....379 10.1. Binary Decisions from Continuous Data: Non-Bayesian Approaches....379 10.2. Point Conditioning....390 10.3. Optimal Bayesian Decision-Making with Continuous Random Variables....395 10.4. Chapter Summary....401 11. Categorical Data, Tests for Dependence, and Goodness of Fit for Discrete Distributions....402 11.1. Tabulating Categorical Data and Creating a Test Statistic....403 11.2. Null Hypothesis Significance Testing for Dependence in Contingency Tables....409 11.3. Chi-Square Goodness-of-Fit Test....415 11.4. Chapter Summary....423 12. Multidimensional Data: Vector Moments and Linear Regression....424 12.1. Summary Statistics for Vector Data....425 12.2. Linear Regression....437 12.3. Null Hypothesis Tests for Correlation....450 12.4. Nonlinear Regression Tests....452 12.5. Chapter Summary....460 13. Working with Dependent Data in Multiple Dimensions....461 13.1. Jointly Distributed Pairs of Random Variables....461 13.2. Standardization and Linear Transformations....471 13.3. Decorrelating Random Vectors and Multi-Dimensional Data....482 13.4. Principal Components Analysis....490 13.5. Chapter Summary....499 Index....500