Bayes’ Theorem

$P(A|B)=\frac{P(A|B)P(A)}{P(B)}$
$P(A|B)$ ⇒ probability of hypothesis A given data B
(posterior belief distribution)

$P(B|A)$ ⇒ likelihood of data B given hypothesis A

$P(A)$ ⇒ independent probability of hypothesis A
(prior belief distribution)

$P(B)$ ⇒ independent probability of data B

Example

Bayes Filter

Probabilistic method to estimate an unknown probability density function (PDF) recursively over time using incoming sensor measurements and a mathematical process model.

Binary Bayes Filter

Probability density function (PDF) of a binary variable.

Task

• Cleaning

• Resteraunte

• Security

• Grid based mapping

Challenges

• Fast Moving Objects

Von Sensor Daten