If you can program, you are ready to grapple with Bayesian statistics. In this book, you'll learn how to solve statistical problems using Python code instead of math formulas, using discrete probability distributions instead of continuous math. Once you get the math out of the way, Bayesian fundamentals become clearer and you begin to apply these techniques to real-world problems.
Bayesian statistical methods are becoming more common and important, but there aren't many resources to help beginners. Based on the undergraduate courses of the author Allen B. Downey, the computational approach of this book will help you to get a solid start.
To start with this book, you must be familiar with Python. If you are familiar with NumPy and pandas this will help, but I'll walk you through what you need to do while doing it. You don't need to know calculus or linear algebra. You do not need any prior knowledge of statistics. In Chapter 1 I define probability and introduce conditional probability, which is the basis of Bayes' theorem. Chapter 3 introduces the probability distribution that forms the basis of Bayesian statistics.
In the following chapters, we use various discrete and continuous distributions, including binomial, exponential, Poisson, beta, gamma, and normal distributions. I'll explain each distribution as it's introduced, and we'll use SciPy to calculate it so you don't have to know its math properties.
Reading this book will not get you very far; To really understand it, you have to work with the code. The original form of this book is a series of Jupyter notebooks. After reading each chapter, I encourage you to read the notebook and work on the exercises. If you need any help, my solutions are at your disposal.
Allen Downey is a professor of computer science at the Olin College of Engineering. He taught computer science at Wellesley College, Colby College, and U.C. Berkeley. He has a PhD. in Computer Science from U.C. Berkeley and Masters and Bachelor degrees from MIT. He is the author of Think Python, Think Bayes, Think DSP, and a blog called "Probably Oarthinking It".
The premise of this book, and the other books in the Think X series, is that once you are comfortable with programming, you can use that skill to learn other subjects.
Most Bayesian statistics books use mathematical notation and present ideas using mathematical concepts such as calculus. This book uses Python code and discrete approximations instead of continuous math. As a result, what would be an integral in a math book becomes a summation, and most operations on probability distributions are loops or array operations.
I think this presentation is easier to understand, at least for people with programming skills. It's also more general because when we make modeling decisions, we can choose the most appropriate model without worrying too much about whether the model is suitable for mathematical analysis. In addition, it provides a smooth path from simple examples to real problems.
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