From Probability to SOTIF

From probability to automated-driving safety.

A beginner-friendly, text-based course that connects the basics of probability and statistics, how machine learning and AI work, and SOTIF (Safety Of The Intended Functionality) and validation for automated driving — in one continuous path.

From probability to SOTIF, published step by step 5–10 minutes per lesson Begins with a math-notation refresher

The question this site is built around

How can we tell that an automated vehicle
is “safe enough”?

Suppose you want to show, from driving records alone, that an automated vehicle causes fatal crashes no more often than human drivers. One estimate says it would have to drive about 440 million km (275 million miles — roughly 11,000 times around the Earth) without a single fatal crash. Driving alone is not enough. So we use probability and statistics to count rare accidents, learn how AI makes mistakes, and apply SOTIF to reduce unknown hazards. This site follows that path.

* Estimate from RAND Corporation, Driving to Safety (2016): the failure-free distance needed to show, with 95% confidence, a fatality rate no worse than the U.S. human-driver rate (1.09 per 100 million miles). Covered in lessons “1.8 Statistics of rare events” and “5.5 Acceptance criteria”.

Learning roadmap

Build up from left to right, and SOTIF at the end becomes something you understand — not something you memorize.

Step 1 Probability & Statistics The language for saying “how safe” in numbers
Step 2 Machine Learning How models learn rules from data, and how to evaluate them
Step 3 Deep Learning & AI What is inside perception AI, and why it succeeds or fails
Step 4 Automated Driving Sensing, thinking and acting — and the ODD
Step 5 SOTIF & Validation Reducing and demonstrating “hazardous without a failure”

If math makes you nervous, start with Part 0 (Getting Started) to review the notation.

Choose your route

You do not have to read everything in order. Pick the card closest to you and start from its button.

New to AI and automated driving

Build up in order, starting with a refresher on probability and statistics. For students, humanities backgrounds and career changers.

Start from the beginning →

Unsure about the math? 0.2 How to read the formulas

I know probability and statistics; I want to learn AI

Learn how machine learning works and how its limits are measured. Go back to Part 1 only when you need it.

Start with Part 2 Machine Learning →

Already know machine learning? Part 3 Deep Learning & AI

I want to understand automated driving and its safety

From how automated driving works to validating its safety with SOTIF. The probability and AI lessons are linked wherever they are needed.

Start with Part 4 Automated Driving →

Already know how automated driving works? Part 5 SOTIF & Validation

Curriculum

English translations are published step by step. Lessons marked “Japanese only” can already be read in Japanese.

NEW Newly published (shown during that month) UPDATE Content revised, e.g. corrections (shown during that month) Coming soon In preparation Japanese only Translation in progress Advanced Optional ▶ Video Video lecture available (click the mark to watch it on YouTube) ▶ Video Video lecture coming soon

Part 0

Getting Started

How to use this site, and a friendly review of math notation.

Part 1

Probability & Statistics

The language for counting uncertainty. At the end, you calculate for yourself how far a car must drive without an accident.

Part 2

Machine Learning Basics

Teaching with data instead of writing rules: how learning works, and how to evaluate it properly.

Part 3

Deep Learning & AI

Look inside perception AI: why it makes mistakes, and how to measure its confidence.

Part 4

How Automated Driving Works

How does an automated vehicle see, think and move? Up to how the three main safety standards relate.

Part 5

SOTIF & Validation

Built around the ideas of ISO 21448: deciding how safe is safe enough, and how to demonstrate it.

Appendix

GlossarySOTIF and machine-learning terms in plain language
NotationHow to read P(A), E[X], σ, ∇ and more
Residual risk in numbersHow the estimate is built from known and unknown hazards, and where each piece is covered
Standards at a glanceISO 26262 / 21448 / PAS 8800 / 34502, UL 4600 and moreComing soon
References and further readingYour next book, and pointers to primary sourcesComing soon
Python notebooksHow to use Google Colab, plus optional exercises you can open in the browserComing soon

AI safety news

News from around the world on AI safety and automated-driving safety, gathered and summarized by an AI agent and checked by Ken before it appears here. Summaries may contain errors, so please check the source articles for details.

Loading the news…

News

2026-10-14: Published the video lectures for “5.2 The four areas” and “5.3 Functional insufficiencies and triggering conditions” (in Japanese and English, on YouTube).
2026-10-13: Published the video lectures for “4.6 Modular vs. end-to-end”, “4.7 Three pillars of safety” and “5.1 What is SOTIF?” (in Japanese and English, on YouTube). Added a section on the design of experiments (orthogonal arrays) and pairwise testing to the advanced part of 5.6.
2026-10-12: Published the video lectures for 4.1–4.5 (in Japanese and English, on YouTube). Added a note on how to set the tail-shape parameter ξ to the advanced section of 1.9.
2026-10-10: Published the video lectures for “3.9 Explainability (XAI)”, “3.10 Metrics for safety”, and “3.11 Testing AI” (in Japanese and English, on YouTube).
2026-10-09: Published the video lectures for “3.7 Uncertainty and calibration” and “3.8 Robustness and adversarial examples” (in Japanese and English, on YouTube).
2026-10-08: Published the video lectures for “3.5 Transformers and attention” and “3.6 Foundation models and generative AI” (in Japanese and English, on YouTube).
2026-10-06: Published the video lectures for “2.8 Data splits and distribution shift” and for “3.1 Neural networks” through “3.4 Object detection and segmentation” (in Japanese and English, on YouTube).
2026-10-05: Published the video lectures for “2.3 Gradient descent” through “2.7 Evaluation metrics” (in Japanese and English, on YouTube).
2026-10-04: Published the video lectures for “2.1 What is machine learning?” and “2.2 Linear regression and loss functions” (in Japanese and English, on YouTube).
2026-10-03: Published the video lectures for “1.6 Estimation and confidence intervals”, “1.7 Hypothesis testing”, “1.8 Statistics of rare events” and “1.9 Extreme values and heavy tails” (in Japanese and English, on YouTube).
2026-10-02: Published the video lecture for “1.3 Probability distributions” (in Japanese and English, on YouTube). Open it from “▶ Video” at the top of the lesson. Published the video lecture for “1.2 Conditional probability and Bayes’ theorem” (in Japanese and English, on YouTube). Published the video lecture for “1.4 Expected value and variance” (in Japanese and English, on YouTube). Published the video lecture for “1.5 Law of large numbers and the central limit theorem” (in Japanese and English, on YouTube).
2026-09-30: Published “3.10 Metrics for safety” and “3.11 Testing AI” (all in Japanese and English). Also added “metrics have a range too” to 2.7 and “evaluating generative AI” to 3.6. Added the miss rate (= 1 − recall) and other names for the metrics (sensitivity, specificity, FNR and so on) to 2.7. Redrew the score-distribution figure in 2.7 with heights in proportion to the counts (the pedestrian hump is a ninth as high).
2026-09-26: Added an “AI safety news” section to the home page (summaries gathered by an AI agent, published after review; also in Japanese). Added a “News” link to the header of every page (marked NEW when there is a new item) and the latest headlines at the top of the home page.
2026-09-24: Revised the simulation example in 5.7 to a realistic number of computers and to the practice of narrowing down with a coarse simulation before checking in detail (also in Japanese).
2026-09-19: Added supplements to 1.1, 1.2, 1.3 and 1.8 that lead into the SOTIF calculations: the two kinds of uncertainty, the weight of a passed test as evidence (likelihood ratio), three properties of the Poisson distribution, and updating prior evidence with mileage (all in Japanese and English). The “Choose your route” section on the home page now shows three cards with an entry button each. Also added the β factor for common causes to 1.1 and exposure weighting to 1.4. The connection box of 1.8 now introduces the probability of a hazard never seen before (the Good–Turing estimate). Also added one-sided upper bounds to 1.6 and a bootstrap section to 1.9. Added the appendix “Residual risk in numbers” (how the estimate is built, mapped to the lessons). Added “how to set the boundary of the ODD” (the rainfall example) to 4.1.
2026-09-18: Added site search (the box in the header finds lesson titles, headings and glossary terms).
2026-09-16: Site created