Intuitive Statistics

Mastering basics, Bayes, and AI

A principled, intuitive introduction to statistical modeling, Bayesian inference, and machine learning.

Author

William D. Pearse

Published

2026

Preface

Intuitive Statistics

It is rare for a biologist to wake up in the middle of the night screaming “I love statistics”. Many would argue that there is nothing wrong with this; I am not quite so sure. If you are a biologist, biology should, of course, be your greatest academic passion. But the brutal reality is that coherent scientific thought requires a coherent scientific thought process, and a solid understanding of statistics is, to my mind, the only practical requirement that all practising empirical scientists share. Without a solid statistical foundation you will find it hard to make a difference in your field.

Most introductory statistics courses focus on passing on a series of incantations that students must learn to invoke when presented with data. Assertions such as “if the histogram of your response variable isn’t Gaussian, you must use non-parametric statistics” are common, unhelpful, and incorrect. No series of arcane rites can guarantee that you will always do the right thing¹. A reliance on such algorithmic statistics means that more advanced courses become essentially impenetrable: there are too many arbitrary decisions that must be held in mind simultaneously without a unifying framework. This complexity is the reason most students claim to hate statistics, when in truth they have never truly taken a course in it.

In this course, I will teach you the fundamental principles underlying most statistical approaches. We will start with the fundamentals of what a probability is and the $t$-test, with which you are likely already familiar, and work up to hierarchical Bayesian models. We will be covering a lot of material, but it is a lot of material that is highly sought-after and valuable. If you pay attention to the general principles, you will have all the skills you need to learn additional statistical techniques on your own, and to reason around unfamiliar tests and approaches. I do not expect you to rote-learn anything.

There will come a time in your career when, because of your focus on general principles, the methods I teach you in this course will become out-of-date. As an example, in this course I teach you the basic use of Hamiltonian Monte Carlo techniques. These were not widely-used in biology when I was a graduate student, but because they derive from the general principles I already knew I am now able to teach a course in them. My aim is to prepare you such that, in ten years time, you will be using all of the concepts, but none of the methods, from this course.

At the end of this handout is a list of books that you may find useful. Some of them may help you during the course (e.g., “The R Book”), others may help you long after (e.g., “Likelihood”). I would be happy if this MSc were the last statistics course you ever took; I would be saddened if it contained the final nuggets of statistics you ever learnt.

This is a corollary of Gödel’s incompleteness theorem, and so is a mathematical ‘fact’↩︎

# Preface {.unnumbered} It is rare for a biologist to wake up in the middle of the night screaming "I love statistics". Many would argue that there is nothing wrong with this; I am not quite so sure. If you are a biologist, biology should, of course, be your greatest academic passion. But the brutal reality is that coherent scientific thought requires a coherent scientific thought process, and a solid understanding of statistics is, to my mind, the only practical requirement that all practising empirical scientists share. Without a solid statistical foundation you will find it hard to make a difference in your field. Most introductory statistics courses focus on passing on a series of incantations that students must learn to invoke when presented with data. Assertions such as "if the histogram of your response variable isn't Gaussian, you must use non-parametric statistics" are common, unhelpful, and incorrect. No series of arcane rites can guarantee that you will always do the right thing^[This is a corollary of Gödel's incompleteness theorem, and so is a mathematical 'fact']. A reliance on such algorithmic statistics means that more advanced courses become essentially impenetrable: there are too many arbitrary decisions that must be held in mind simultaneously without a unifying framework. This complexity is the reason most students claim to hate statistics, when in truth they have never truly taken a course in it. In this course, I will teach you the fundamental principles underlying most statistical approaches. We will start with the fundamentals of what a probability is and the $t$-test, with which you are likely already familiar, and work up to hierarchical Bayesian models. We will be covering a lot of material, but it is a lot of material that is highly sought-after and valuable. If you pay attention to the *general principles*, you will have all the skills you need to learn additional statistical techniques on your own, and to reason around unfamiliar tests and approaches. I do not expect you to rote-learn anything. There will come a time in your career when, because of your focus on general principles, the methods I teach you in this course will become out-of-date. As an example, in this course I teach you the basic use of Hamiltonian Monte Carlo techniques. These were not widely-used in biology when I was a graduate student, but because they derive from the general principles I already knew I am now able to teach a course in them. My aim is to prepare you such that, in ten years time, you will be using all of the concepts, but none of the methods, from this course. At the end of this handout is a list of books that you may find useful. Some of them may help you during the course (*e.g.*, "The R Book"), others may help you long after (*e.g.*, "Likelihood"). I would be happy if this MSc were the last statistics course you ever took; I would be saddened if it contained the final nuggets of statistics you ever learnt.