The Historical Evolution and Paradigm Shift of Mathematical Statistics Theory - The Theoretical Trajectory from Descriptive Statistics to Data Science

Abstract

In the past 100 years, mathematical statistics has undergone great changes in theory. It has changed from a science that only describes numbers to a science that can predict and provide suggestions, which is very helpful for today’s data decision. This study reports that the history of statistical theory is divided into four main stages: first, the classical period of descriptive statistics and probability basis; Followed by Fisher, Neyman and Pearson’s statistical testing revolution. Then, Bayesian regression and ideas about decision; Finally, today’s data science has an algorithm model, a large number of dimensions of analysis and computer learning. Using the insights of probability theory, philosophy of science, computer science and applied mathematics, we have constructed a story, showing the consistent content and completely changed content in the theory. Our analysis shows that each paradigm shift is driven by the relationship between mathematical innovation, computing power and practical application requirements. At present, the transformation from model-based reasoning to algorithm-based prediction is not only a technical improvement, but also a new way of thinking, which can be learned from data. This study provides a complete map of the history of statistical thinking, shows the tension between frequency and Bayesian epistemology, and provides a framework to better understand how statistical theory and data science change together.