Book Image

Principles of Data Science

Book Image

Principles of Data Science

Overview of this book

Need to turn your skills at programming into effective data science skills? Principles of Data Science is created to help you join the dots between mathematics, programming, and business analysis. With this book, you’ll feel confident about asking—and answering—complex and sophisticated questions of your data to move from abstract and raw statistics to actionable ideas. With a unique approach that bridges the gap between mathematics and computer science, this books takes you through the entire data science pipeline. Beginning with cleaning and preparing data, and effective data mining strategies and techniques, you’ll move on to build a comprehensive picture of how every piece of the data science puzzle fits together. Learn the fundamentals of computational mathematics and statistics, as well as some pseudocode being used today by data scientists and analysts. You’ll get to grips with machine learning, discover the statistical models that help you take control and navigate even the densest datasets, and find out how to create powerful visualizations that communicate what your data means.
Table of Contents (20 chapters)
Principles of Data Science
Credits
About the Author
About the Reviewers
www.PacktPub.com
Preface
Index

Bayesian ideas revisited


In the last chapter, we talked, very briefly, about Bayesian ways of thinking. In short, when speaking about Bayes, you are speaking about the following three things and how they all interact with each other:

  • A prior distribution

  • A posterior distribution

  • A likelihood

Basically, we are concerned with finding the posterior. That's the thing we want to know.

Another way to phrase the Bayesian way of thinking is that data shapes and updates our belief. We have a prior probability, or what we naively think about a hypothesis, and then we have a posterior probability, which is what we think about a hypothesis, given some data.

Bayes theorem

Bayes theorem is the big result of Bayesian inference. Let's see how it even comes about. Recall that we previously defined the following:

  • P(A) = The probability that event A occurs

  • P(A|B) = The probability that A occurs, given that B occurred

  • P(A, B) = The probability that A and B occurs

  • P(A, B) = P(A) * P(B|A)

That last bullet can be read as...