Statistics for Machine Learning with Mathematica Applications

TL;DR

This paper explores the integration of statistical methods with Mathematica, providing theoretical foundations, practical examples, and extensive code to facilitate data analysis, hypothesis testing, and probabilistic modeling across various scientific disciplines.

Contribution

It offers a comprehensive collection of over 200 statistical manipulations, 500 Mathematica code examples, and 25 programs, all based on core statistical theorems and principles.

Findings

Extensive Mathematica code library for statistical analysis.

Practical tools for hypothesis testing and estimation.

Facilitates data-driven discoveries across disciplines.

Abstract

In recent years, the field of statistics has experienced a surge in interest and application, largely due to significant advances in computer technology. This progress has led to remarkable developments in statistics methods and algorithms, enabling their widespread adoption across various disciplines. Key areas benefiting from these advancements include machine learning, economics, finance, geophysics, molecular modeling, computational systems biology, operations research, and engineering. For example, in machine learning, statistics forms the foundation for algorithms used in regression, classification, clustering, and deep learning to analyze vast datasets and make predictions. Mathematica, among other tools, has played a significant role in enabling the integration of statistics and computer technology, facilitating deeper exploration of data-driven insights and groundbreaking discoveries across diverse domains. With a rich library of functions, Mathematica allows users to calculate measures of central tendency, dispersion, and correlation, as well as perform hypothesis testing and estimation. Moreover, it supports probability distributions, making simulations and probabilistic modeling tasks more accessible. This monograph presents the main theorems in mathematical statistics, ranging from basic descriptive statistics to sophisticated inferential techniques. In addition, we have created, more than 200 manipulates cover different scenarios in statistics, more than 500 light Mathematica codes (examples) and 25 programs (procedures) that follow the principles of testing hypotheses and estimation theory. The code will run as-is with no code from prior algorithms or third parties required beyond the installation of Mathematica.