Preface

Statistics is a discipline of study used for applying analytical methods to answer questions and solve problems using data, in both academic and industry settings. Many methods have been around for centuries, while others are much more recent. Statistical analysis and results are fairly straightforward for presenting to both technical and non-technical audiences. Furthermore, producing results with statistical analysis does not necessarily require large amounts of data or compute resources and can be done fairly quickly, especially when using programming languages such as Python, which is moderately easy to work with and implement.

While artificial intelligence (AI) and advanced machine learning (ML) tools have become more prominent and popular over recent years with the increase of accessibility in compute power, performing statistical analysis as a precursor to developing larger-scale projects using AI and ML can enable a practitioner to assess feasibility and practicality before using larger compute resources and project architecture development for those types of projects.

This book provides a wide variety of tools that are commonly used to test hypotheses and provide basic predictive capabilities to analysts and data scientists alike. The reader will walk through the basic concepts and terminology required for understanding the statistical tools in this book prior to exploring the different tests and conditions under which they are applicable. Further, the reader will gain knowledge for assessing the performance of the tests. Throughout, examples will be provided in the Python programming language to get readers started understanding their data using the tools presented, which will be applicable to some of the most common questions faced in the data analytics industry. The topics we will walk through include:

• An introduction to statistics
• Regression models
• Classification models
• Time series models
• Survival analysis

Understanding the tools provided in these sections will provide the reader with a firm foundation from which further independent growth in the statistics domain can more easily be achieved.

Who this book is for

Professionals in most industries can benefit from the tools in this book. The tools provided are useful primarily at a higher level of inferential analysis, but can be applied to deeper levels depending on the industry in which the practitioner wishes to apply them. The target audiences of this book are:

• Industry professionals with limited statistical or programming knowledge who would like to learn to use data for testing hypotheses they have in their business domain
• Data analysts and scientists who wish to broaden their statistical knowledge and find a set of tools and their implementations for performing various data-oriented tasks

The ground-up approach of this book seeks to provide entry into the knowledge base for a wide audience and therefore should neither discourage novice-level practitioners nor exclude advanced-level practitioners from the benefits of the materials presented.

What this book covers

Chapter 1, Sampling and Generalization, describes the concepts of sampling and generalization. The discussion of sampling covers several common methods for sampling data from a population and discusses the implications for generalization. This chapter also discusses how to setup the software required for this book.

Chapter 2, Distributions of Data, provides a detailed introduction to types of data, common distributions used to describe data, and statistical measures. This chapter also covers common transformations used to change distributions.

Chapter 3, Hypothesis Testing, introduces the concept of statistical tests as a method for answering questions of interest. This chapter covers the steps to perform a test, the types of errors encountered in testing, and how to select power using the Z-test.

Chapter 4, Parametric Tests, further discusses statistical tests, providing detailed descriptions of common parametric statistical tests, the assumptions of parametric tests, and how to assess the validity of parametric tests. This chapter also introduces the concept of multiple tests and provides details on corrections for multiple tests.

Chapter 5, Non-parametric Tests, discuss how to perform statistical tests when the assumptions of parametric tests are violated with class of tests without assumptions called non-parametric tests.

Chapter 6, Simple Linear Regression, introduces the concept of a statistical model with the simple linear regression model. This chapter begins by discussing the theoretical foundations of simple linear regression and then discusses how to interpret the results of the model and assess the validity of the model.

Chapter 7, Multiple Linear Regression, builds on the previous chapter by extending the simple linear regression model into additional dimensions. This chapter also discusses issues that occur when modeling with multiple explanatory variables, including multicollinearity, feature selection, and dimension reduction.

Chapter 8, Discrete Models, introduces the concept of classification and develops a model for classifying variables into discrete levels of a categorical response variable. This chapter starts by developing the model binary classification and then extends the model to multivariate classification. Finally, the Poisson model and negative binomial models are covered.

Chapter 9, Discriminant Analysis, discusses several additional models for classification, including linear discriminant analysis and quadratic discriminant analysis. This chapter also introduces Bayes’ Theorem.

Chapter 10, Introduction to Time Series, introduces time series data, discussing the time series concept of autocorrelation and the statistical measures for time series. This chapter also introduces the white noise model and stationarity.

Chapter 11, ARIMA Models, discusses models for univariate models. This chapter starts by discussing models for stationary time series and then extends the discussion to non-stationary time series. Finally, this chapter provides a detailed discussion on model evaluation.

Chapter 12, Multivariate Time Series, builds on the previous two chapters by introducing the concept of a multivariate time series and extends ARIMA models to multiple explanatory variables. This chapter also discusses time series cross-correlation.

Chapter 13, Survival Analysis, introduces survival data, also called time-to-event data. This chapter discusses the concept of censoring and the impact of censoring survival data. Finally, the chapter discusses the survival function, hazard, and hazard ratio.

Chapter 14, Survival Models, building on the previous chapter, provides an overview of several models for survival data, including the Kaplan-Meier model, the Exponential model, and the Cox Proportional Hazards model.

To get the most out of this book

You will need access to download and install open-source code packages implemented in the Python programming language and accessible through PyPi.org or the Anaconda Python distribution. While a background in statistics is helpful, but not necessary, this book assumes you have a decent background in basic algebra. Each unit of this book is independent of the other units, but the chapters within each unit build upon each other. Thus, we advise you to begin each unit with that unit’s first chapter to understand the content.

Software/hardware covered in the book	Operating system requirements
Python version ≥ 3.8	Windows, macOS, or Linux
Statsmodels 0.13.2
SciPy 1.8.1
lifelines 0.27.4
scikit-learn 1.1.1
pmdarima 2.02
Sktime 0.15.0
Pandas 1.4.3
Matplotlib 3.5.2
Numpy 1.23.0

If you are using the digital version of this book, we advise you to type the code yourself or access the code from the book’s GitHub repository (a link is available in the next section). Doing so will help you avoid any potential errors related to the copying and pasting of code.

Download the example code files

You can download the example code files for this book from GitHub at https://github.com/PacktPublishing/Building-Statistical-Models-in-Python. If there’s an update to the code, it will be updated in the GitHub repository.

We also have other code bundles from our rich catalog of books and videos available at https://github.com/PacktPublishing/. Check them out!

Conventions used

There are a number of text conventions used throughout this book.

Code in text: Indicates code words in text, database table names, folder names, filenames, file extensions, pathnames, dummy URLs, user input, and Twitter handles. Here is an example: “Mount the downloaded WebStorm-10*.dmg disk image file as another disk in your system.”

A block of code is set as follows:

A = [3,5,4]
B = [43,41,56,78,54]
permutation_testing(A,B,n_iter=10000)

Any command-line input or output is written as follows:

pip install SomePackage

Bold: Indicates a new term, an important word, or words that you see onscreen. For instance, words in menus or dialog boxes appear in bold. Here is an example: “Select System info from the Administration panel.”

Tips or important notes

Appear like this.

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