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W05. Control 04

Today is an introduction to probability and predictions that are useful in control. Robots live in a probabilistic world, i.e., there is never 100% certainty about the correspondence between their model of the world, and the world itself. This is due to the presence of error: nothing is perfectly precise, therefore none of our models can be perfectly deterministic.

In many cases, as we saw with the threshold filter, "good enough" is good enough. But when it comes to long-term decision-making, errors accumulate, and then "good enough" quickly becomes "not very good at all."

Even if you have learned probability and statistics before, it's hard to figure out how to use probability in an application such as robotics. Today, we'll learn basic statistics and basic probability with applications to robotic control so that when we use it later, we have a solid foundation to build on.

Pre-readings and Videos​

Because we're introducing probability (and this is not a math class), you will have to do some work to understand some of the symbols and ideas that we're using. Robots need to leverage probability to act in the world, and there's a lot of evidence that humans are often acting with something like a probability "in mind" when predicting events (although likely not a literal number). The reading introduces the mathematics in a nice visual way, and the video introduces common cogntive approaches to evaluating probabilities in real life.

Intro to Probability and Stats​

Seeing Theory: A Visual Introduction to Probability and Statistics is an excellent way to get an intuition for probability. We suggest playing around with the interactive widgets until you're able to explain them confidently to someone else.

This book stops just short of Bayes, but the conditional probability section gives you everything you need to understand why it's possible to use Bayes Theorem.

Black Swan Events​

Nicholas Taleb introduces his way of thinking about probability and seemingly unlikely events.

Summary of the Day​

Learning Goals​

  1. Be able to count outcomes to model the probability of simple events.
  2. Be able to write and use the formulas for compound events, including conditional probability.
  3. Be able to describe simple summary statistics such as mean, median, and standard deviation.