16. Conditional Distributions
Nd787 C4 L1 A12 Conditional Distributions V1
Summary of Notation
| Notation | Mathematical Meaning |
|---|---|
| p(x) | The probability of x |
| p(x,y) | The probability of x and y |
| p(x | y) |
| p(y | x) |
In the example from the video, we took x to be the vehicle position and y to be the sensor measurements. With this in mind, this notation takes on some real world meaning.
| Notation | "Real world" Meaning |
|---|---|
| p(x) | The probability of the vehicle being in position x. |
| p(x,y) | The probability of the vehicle being in position x and making measurements y. |
| p(x | y) |
| p(y | x) |
When we do estimation for a flying vehicle, we generally have access to the measurements y and we want to know the probability of x given those measurements. So we want to calculate p(x|y).
But it turns out that it's often MUCH easier to generate the distribution of measurement likelihoods given the current position. That is, it's easier to come up with p(y|x) than it is to come up with p(x|y). This is where Bayes' Rule is really helpful! According to Bayes' Rule:
p(x|y) = \frac{p(y|x)p(x)}{p(y)}