AI Publishing - Statistics Crash Course for Beginners: Theory and Applications of Frequentist and Bayesian Statistics Using Python

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First Printing, 2020

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Published by AI Publishing LLC

ISBN-13: 978-1-7347901-6-0

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Table of Contents

Preface

The fields of Artificial Intelligence (AI), Machine Learning (ML), and Data Science (DS) are prevailing in many real-world applications. A crucial part of these fields is to deal with a huge amount of data, which is produced at an unprecedented rate nowadays. This data is used to extract useful information for making future predictions on unseen but similar kinds of data.

Statistics is the field that lies at the core of Artificial Intelligence, Machine Learning, and Data Science. Statistics is concerned with collecting, analyzing, and understanding data. It aims to develop models that are able to make decisions in the presence of uncertainty. Numerous techniques of the aforementioned fields make use of statistics. Thus, it is essential to gain knowledge of statistics to be able to design intelligent systems.

This book is dedicated to the techniques for frequentist and Bayesian statistics. These two types of statistical techniques interpret the concept of probability in different ways.

According to the frequentist approach, the probability of an event is defined for the repeatable events whose outcomes are random. The statistical experiment is run again and again in a long run to get the probability of the event. Thus, the probability of an event equals the long-term frequency of occurrence of that event.

For example, rolling a six-sided dice can be considered a repeatable statistical experiment. The outcome of this experiment can be any number from 1 to 6. Since we do not know what will be the outcome in a particular rolling of the dice, we call it a random outcome. According to the frequentist approach, the chance of getting any particular number from 1 to 6 is equally likely. In other words, the probability of any number is 1/6 or 1 out of 6.

As another example, in a pack of 52 cards, we randomly draw a card. We want to check the chance of getting a king. To find the probability of our defined event, i.e., getting a king, we count the number of favorable outcomes: 4 out of 52 cards. Thus, the probability of getting a king is obtained by dividing the number of favorable outcomes by the total number of possible outcomes: 4/52 = 1/13.

The frequentist way of doing statistics makes use of the data from the current experiment. However, contrary to the frequentist approach, the Bayesian approach interprets probability as a degree of belief. For example, it is believed from some previous experiments that a head is twice as likely to occur than a tail. Now, the probability of having a head would be 2/3 as compared to the probability of getting a tail, i.e., 1/3. This belief before running the experiment is our prior belief about the experiment of tossing a coin.

The belief can increase, decrease, or even remain the same if we run this experiment again and again. This example shows that the Bayesian interpretation of probability makes use of previous runs of the experiment to have a degree of belief about any particular experiment. We shall go into the details of these concepts in subsequent chapters of the book.

This book intends to teach beginners the concepts of statistics using the Python programming language. After completing the book, the readers will learn how to collect, sample, manipulate, and analyze data. They will also perform experiments to explore and visualize a given dataset. The book aims to introduce to the reader the techniques for estimation and inference of valuable parameters of the statistical models.