An introduction to statistical modeling through Python implementation

Summary

Python will be a general-purpose programming language with many excellent features, such as being easy to learn, easy to write readable code, and usable for a wide range of applications Python was developed by Guido van Rossum in 1991.

As a relatively new language, Python can utilize a variety of effective programming techniques, including object-oriented programming, procedural programming, and functional programming. It is also widely used in web applications, desktop applications, scientific and technical computing, machine learning, artificial intelligence, and other fields because of the many libraries and frameworks available. Furthermore, it is cross-platform and runs on many operating systems such as Windows, Mac, and Linux, etc. Because Python is an interpreted language, it does not require compilation and has a REPL-like structure, which speeds up the development cycle.

This section discusses statistical modeling using python based on the “Introduction to Statistical Modeling, – Learning through Python Implementation“.

Here we discuss the reading notes.

An introduction to statistical modeling through Python implementation

This book provides an overview of the theory of machine learning with probability and its implementation in pyhon.

The contents are as follows

Chapter 1 Probability Distribution and Maximum Likelihood Method
1.1 Intuitive understanding and definition of probability distribution and its application
1.1.1 Intuitive Understanding of Probability Distribution (Normal Distribution) by Sampling
1.1.2 Probability Distributions Learned with Formulas
Probability Density Function and Cumulative Distribution Function
NormalDistribution
PoissonDistribution
Binomial Distribution (Binomialdistribution)
1.2 Probability Distributions and Statistical Modeling
1.3 Probability distribution and maximum likelihood method
1.3.1 Probability Distributions and Parameters
1.3.2 Simultaneous Probability and Likelihood
1.3.3 Maximum Likelihood Method
Maximum Likelihood Estimation of Bernoulli Distribution
Maximum Likelihood Estimation of Poisson Distribution
Maximum Likelihood Estimation for Normal Distribution
Summary

Chapter 2 Generalized Linear Models
2.1 Generalized Linear Models
2.2 Exponential Family of Distributions
2.2.1 Definition of Exponential Family of Distributions and Normal Distribution
2.2.2 Definition of exponential family of distributions and Bernoulli distribution
2.2.3 Definition of Exponential Family of Distributions and Poisson Distribution
2.3 Specific Examples of Generalized Linear Models
2.3.1 Logistic Regression
Problem Setup
Implementation Policy
Implementation
2.3.2 Poisson Regression
Problem setting
Implementation Policy
Implementation
2.4 On the Maximum Likelihood Method and Error Functions
2.4.1 The Least Squares Method Derived from the Maximum Likelihood Method
2.4.2 Cross-Entropy Errors and the Maximum Likelihood Method

Chapter 3 Maximum Likelihood and Bayesian Statistical Modeling
3.1 Maximum Likelihood and Sample Size
3.2 Bayes' Theorem and Prior and Posterior Distributions
3.3 MAP Inference for Weighted Parameters
3.4 Derivation of Predictive Distributions
3.4.1 Checking the equations
3.4.2 Problem Setup* 3.4.3 Implementation
3.4.3 Implementation

Chapter 4 Optimization and the MCMC Method
4.1 Reviewing Optimization Again
4.1.1 Many optimization problems can be replaced by maximum or minimum value problems.
4.1.2 The discussion of convexity of a function is important, but it is best to grasp it in the image of a quadratic function.
4.1.3 There are two major approaches to solving the maximum or minimum value problem: 1. Solve the equation, and 2. Solve the equation by iterative operations using a computer.
4.2 Gradient Descent Method
4.2.1 Example and Gradient Descent Method
Example problem
Solution to the example problem
Explanation
4.2.2 Gradient method and curve fitting
Solving mathematically (normal equations)
Solving with the gradient descent method (numerical)
4.3 MCMC Method
4.3.1 What is the MCMC method?
4.3.2 Metropolis-Hastings method
4.3.3 Logistic regression problem definition (refresher)
4.3.4 Understanding Logistic Regression with MCMC through Implementation
About this book
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