Book Image

Applying Math with Python - Second Edition

By : Sam Morley
Book Image

Applying Math with Python - Second Edition

By: Sam Morley

Overview of this book

The updated edition of Applying Math with Python will help you solve complex problems in a wide variety of mathematical fields in simple and efficient ways. Old recipes have been revised for new libraries and several recipes have been added to demonstrate new tools such as JAX. You'll start by refreshing your knowledge of several core mathematical fields and learn about packages covered in Python's scientific stack, including NumPy, SciPy, and Matplotlib. As you progress, you'll gradually get to grips with more advanced topics of calculus, probability, and networks (graph theory). Once you’ve developed a solid base in these topics, you’ll have the confidence to set out on math adventures with Python as you explore Python's applications in data science and statistics, forecasting, geometry, and optimization. The final chapters will take you through a collection of miscellaneous problems, including working with specific data formats and accelerating code. By the end of this book, you'll have an arsenal of practical coding solutions that can be used and modified to solve a wide range of practical problems in computational mathematics and data science.
Table of Contents (13 chapters)

Analyzing conversion rates with Bayesian techniques

Bayesian probability allows us to systematically update our understanding (in a probabilistic sense) of a situation by considering data. In more technical language, we update the prior distribution (our current understanding) using data to obtain a posterior distribution. This is particularly useful, for example, when examining the proportion of users who go on to buy a product after viewing a website. We start with our prior belief distribution. For this, we will use the beta distribution, which models the probability of success given a number of observed successes (completed purchases) against failures (no purchases). For this recipe, we will assume that our prior belief is that we expect 25 successes from 100 views (75 fails). This means that our prior belief follows a beta (25, 75) distribution. Let’s say that we wish to calculate the probability that the true rate of success is at least 33%.

Our method is roughly divided...