Book Title: A minimal introduction to probability theory, statistical inference and hypothesis testing

Book Description

This book offers a coherent introduction to probability, statistics, and hypothesis testing, tracing a single line of reasoning from the first principles of data description to the algorithms shaping modern artificial intelligence. It opens with the basics of sampling, estimation, and visualization, then builds the probabilistic foundations needed to reason about uncertainty, before turning to the machinery of statistical inference: the laws that make estimation reliable, the logic of hypothesis testing, and the models that describe how variables relate to one another. From there, the book turns to Bayesian reasoning as an alternative way of updating belief in light of evidence, and closes with Markov processes, tracing a direct line from a nineteenth-century dispute over free will to the Markov chains, Monte Carlo methods, and transformer architectures underlying today’s machine learning systems. Throughout, mathematical rigor is paired with historical context, situating each idea within the lives and debates of the mathematicians who developed it, while appendices on linear algebra and calculus provide the tools needed to follow the arguments in full. The result is a text that treats probability and statistics not as a fixed toolkit, but as a living body of ideas still being written today.