Book Image

Building Statistical Models in Python

By : Huy Hoang Nguyen, Paul N Adams, Stuart J Miller
Book Image

Building Statistical Models in Python

By: Huy Hoang Nguyen, Paul N Adams, Stuart J Miller

Overview of this book

The ability to proficiently perform statistical modeling is a fundamental skill for data scientists and essential for businesses reliant on data insights. Building Statistical Models with Python is a comprehensive guide that will empower you to leverage mathematical and statistical principles in data assessment, understanding, and inference generation. This book not only equips you with skills to navigate the complexities of statistical modeling, but also provides practical guidance for immediate implementation through illustrative examples. Through emphasis on application and code examples, you’ll understand the concepts while gaining hands-on experience. With the help of Python and its essential libraries, you’ll explore key statistical models, including hypothesis testing, regression, time series analysis, classification, and more. By the end of this book, you’ll gain fluency in statistical modeling while harnessing the full potential of Python's rich ecosystem for data analysis.

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Table of Contents (22 chapters)
Preface
Preface
Who this book is for
What this book covers
To get the most out of this book
Download the example code files
Conventions used
Get in touch
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1
Part 1:Introduction to Statistics
Part 1:Introduction to Statistics
Free Chapter
2
Chapter 1: Sampling and Generalization
Chapter 1: Sampling and Generalization
Software and environment setup
Population versus sample
Population inference from samples
Sampling strategies – random, systematic, stratified, and clustering
Summary
3
Chapter 2: Distributions of Data
Chapter 2: Distributions of Data
Technical requirements
Understanding data types
Measuring and describing distributions
The normal distribution and central limit theorem
Bootstrapping
Permutations
Transformations
Summary
References
4
Chapter 3: Hypothesis Testing
Chapter 3: Hypothesis Testing
The goal of hypothesis testing
Type I and Type II errors
Basics of the z-test – the z-score, z-statistic, critical values, and p-values
Summary
5
Chapter 4: Parametric Tests
Chapter 4: Parametric Tests
Assumptions of parametric tests
T-test – a parametric hypothesis test
Tests with more than two groups and ANOVA
Summary
References
6
Chapter 5: Non-Parametric Tests
Chapter 5: Non-Parametric Tests
When parametric test assumptions are violated
The Rank-Sum test
The Signed-Rank test
The Kruskal-Wallis test
Chi-square distribution
Chi-square goodness-of-fit
Chi-square test of independence
Chi-square goodness-of-fit test power analysis
Spearman’s rank correlation coefficient
Summary
7
Part 2:Regression Models
Part 2:Regression Models
8
Chapter 6: Simple Linear Regression
Chapter 6: Simple Linear Regression
Simple linear regression using OLS
Coefficients of correlation and determination
Required model assumptions
Testing for significance and validating models
Summary
9
Chapter 7: Multiple Linear Regression
Chapter 7: Multiple Linear Regression
Multiple linear regression
Feature selection
Shrinkage methods
Dimension reduction
Summary
10
Part 3:Classification Models
Part 3:Classification Models
11
Chapter 8: Discrete Models
Chapter 8: Discrete Models
Probit and logit models
Multinomial logit model
Poisson model
The negative binomial regression model
Summary
12
Chapter 9: Discriminant Analysis
Chapter 9: Discriminant Analysis
Bayes’ theorem
Linear Discriminant Analysis
Quadratic Discriminant Analysis
Summary
13
Part 4:Time Series Models
Part 4:Time Series Models
14
Chapter 10: Introduction to Time Series
Chapter 10: Introduction to Time Series
What is a time series?
Goals of time series analysis
Statistical measurements
The white-noise model
Stationarity
Summary
References
15
Chapter 11: ARIMA Models
Chapter 11: ARIMA Models
Technical requirements
Models for stationary time series
Models for non-stationary time series
Seasonal ARIMA models
More on model evaluation
Summary
References
16
Chapter 12: Multivariate Time Series
Chapter 12: Multivariate Time Series
Multivariate time series
ARIMAX
VAR modeling
Summary
References
17
Part 5:Survival Analysis
Part 5:Survival Analysis
18
Chapter 13: Time-to-Event Variables – An Introduction
Chapter 13: Time-to-Event Variables – An Introduction
What is censoring?
Survival data
Survival Function, Hazard and Hazard Ratio
Summary
19
Chapter 14: Survival Models
Chapter 14: Survival Models
Technical requirements
Kaplan-Meier model
Exponential model
Cox Proportional Hazards regression model
Summary
20
Index
Index
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21
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When parametric test assumptions are violated

In the previous chapter, we discussed parametric tests. Parametric tests have strong statistical power but also require adherence to strong assumptions. When the assumptions are not satisfied, the test results are not valid. Fortunately, we have alternative tests that can be used when the assumptions of a parametric test are not satisfied. These tests are called non-parametric tests, meaning that they make no assumptions about the underlying distribution of the data. While non-parametric tests do not require distributional assumptions, these tests will still require the samples to be independent.

Permutation tests

For the first non-parametric test, let’s look more deeply at the definition of a p-value. A p-value is the probability of obtaining a test statistic at least as extreme as the observed value under the assumption of the null hypothesis. Then, to calculate a p-value, we need the null distribution and an observed statistic...

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