W06. State 01
Today we will learn about Bayes Theorem, and how to apply it to detection in robotics. It is foundational to many techniques in robotics from basic detection, to building complex machine learning classifiers.
At its core, Bayes Theorem is just a statement about conditional probability, which we learned about last time. The more information we know about a situation that a robot will find itself in, the more confident we can be about our predictions.
Our application area will be wall-following, in particular, trying to detect whether we're coming up to a corner. We'll integrate our prior knowledge about the corner with our observations of the robot's position to make a decision about where to go.
Pre-readings and Videos
Bayesian thinking is foundational to many fields and is used operationally in robotics. The first resource will teach you about the basic idea of Bayes, and the second shows a way that Bayes is applied as a conceptual model for cognition.
Introduction to Bayes
Visualizing Bayes Theorem is a great resource for Bayes, which, in essence, is just a statement about conditional probability where we rearrange the known and unknown parts of an equation. It seems a bit like magic, but all we're doing with Bayes is estimating an unknown condition.
Do Babies use Bayesian Thinking?
Allison Gopnik believes that babies use a kind of inductive reasoning that operates in a similar fasion to Bayes theorem. They seem to test interconnected "hypotheses" about the world by integrating evidence gained through observation.
Summary of the Day
- Lesson. Bayes Theorem.
- Class notes. Available here
Learning Goals
- Use Bayes Theorem to model common robotics state estimation problems.
- Explain how Bayes is used to estimate unknown state from known state.
- Differentiate an analytical and experimental approach to Bayes.