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15 Math Concepts Every Data Scientist Should Know

You're reading from   15 Math Concepts Every Data Scientist Should Know Understand and learn how to apply the math behind data science algorithms

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Product type Paperback
Published in Aug 2024
Publisher Packt
ISBN-13 9781837634187
Length 510 pages
Edition 1st Edition
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Author (1):
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David Hoyle David Hoyle
Author Profile Icon David Hoyle
David Hoyle
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Table of Contents (21) Chapters Close

Preface 1. Part 1: Essential Concepts
2. Chapter 1: Recap of Mathematical Notation and Terminology FREE CHAPTER 3. Chapter 2: Random Variables and Probability Distributions 4. Chapter 3: Matrices and Linear Algebra 5. Chapter 4: Loss Functions and Optimization 6. Chapter 5: Probabilistic Modeling 7. Part 2: Intermediate Concepts
8. Chapter 6: Time Series and Forecasting 9. Chapter 7: Hypothesis Testing 10. Chapter 8: Model Complexity 11. Chapter 9: Function Decomposition 12. Chapter 10: Network Analysis 13. Part 3: Selected Advanced Concepts
14. Chapter 11: Dynamical Systems 15. Chapter 12: Kernel Methods 16. Chapter 13: Information Theory 17. Chapter 14: Non-Parametric Bayesian Methods 18. Chapter 15: Random Matrices 19. Index 20. Other Books You May Enjoy

Summary

The focus of this chapter has been hypothesis testing. The chapter contained only three sections, but those sections contained a wealth of new ideas and concepts. Most of the new concepts centered around p-values – what they are, what they are not, how we calculate them, and how we interpret them. These are concepts that you must get to grips with as a working data scientist. To get to grips with them, we specifically learned about the following,

  • How a hypothesis test consists of two hypotheses, the null hypothesis <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:m="http://schemas.openxmlformats.org/officeDocument/2006/math"><mml:msub><mml:mrow><mml:mi mathvariant="script">H</mml:mi></mml:mrow><mml:mrow><mml:mn>0</mml:mn></mml:mrow></mml:msub></mml:math> and the alternative hypothesis <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:m="http://schemas.openxmlformats.org/officeDocument/2006/math"><mml:msub><mml:mrow><mml:mi mathvariant="script">H</mml:mi></mml:mrow><mml:mrow><mml:mn>1</mml:mn></mml:mrow></mml:msub></mml:math>, and how we calculate the p-value as the probability of getting the observed test statistic, or larger, if the null hypothesis is true.
  • How we use the numerical value of the p-value in comparison to a small threshold value, <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:m="http://schemas.openxmlformats.org/officeDocument/2006/math"><mml:mi>α</mml:mi></mml:math>, as evidence to reject the null hypothesis and accept the alternative hypothesis
  • How the threshold <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:m="http://schemas.openxmlformats.org/officeDocument/2006/math"><mml:mi>α</mml:mi></mml:math> controls the false positive rate of the hypothesis test
  • What the p-value is and what...
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