Quantitative Approaches in Modern Biology
BIO 165/265 — Lecture Script
Welcome
BIO 165/265 · Stanford University
Quantitative Approaches in Modern Biology
Quantitative methods and statistics to analyze cell, molecular, and organismal biology.
Welcome to BIO165/265
For beginners. This course is for biology students with little background in coding, mathematics, or statistics. We introduce every concept step by step and focus on the conceptual logic rather than on mathematical proofs. We apply each concept or method to real biological data in Python-based dry labs. If much of this is new to you, plan to invest time: getting comfortable with coding and quantitative reasoning takes practice, especially in the first weeks. We will guide you through it with these detailed notes, the dry labs, tutorials, and office hours. The potential reward is substantial: quantitative skills are increasingly central to modern, data-rich biology, and this course provides a foundation from which you can develop them further.
A guiding principle: from coin tosses to cells. Fundamental statistical ideas in biology can be understood through the simplest random experiment there is — tossing a coin. We will therefore return to the coin toss repeatedly throughout this course to illustrate why averages become reliable (law of large numbers), how uncertain an estimate is (standard error, bootstrapping), and how to decide whether a difference is real (is the coin fair?). The same counting logic then describes sequencing reads and molecule numbers (counting statistics) and the stochastic gene expression of individual cells (stochastic processes).
AI as an opportunity to promote quantitative analysis. We encourage the use of AI tools in this course. Large language models can help substantially with coding, debugging, and exploring analysis approaches, and they make quantitative analysis more accessible than ever before — a real opportunity, especially if you are new to coding. At the same time, it is essential to maintain conceptual control: understand what each analysis step does and why, check AI-generated code and results critically, and judge whether an outcome makes biological and statistical sense. See Use of AI tools for our recommendations and the course policy.
Lecture Notes. This website contains detailed lecture notes that support the in-class lectures and provide additional context and detail. The notes are still under active development: we have newly put them together for this year’s course and continue to extend and improve them. Your feedback is highly appreciated — please let us know about typos, unclear explanations, or suggestions for improvement. Contact Jonas Cremer or open an issue on GitHub.
Jonas Cremer, March 2026
The course, week by week
Data & models Statistics Dynamics (optional)
Week 1 Introduction & getting started
Week 2 Biological data
Week 3 Fitting and regression
Week 4 Probability and uncertainty
Week 5 Hypothesis testing
Week 6 Counting statistics
Week 7 Omics and high-dimensional data
Week 8 Optional Dynamical and stochastic systems
Week 9 Optional Nonlinear dynamics