1
$\begingroup$

I'm a bit stuck trying to figure out the combined probability from several discrete PDF's.

Lets say I have a bunch of different classes (Truck, Sports Car, Station Wagon, etc) and a bunch of different scenarios I've worked out from my dataset (Location, behaviour, size, heading, speed).

Probability that the vehicle at the position x,y (Golf course) is a:

  • Truck: 0.1
  • Sports Car: 0.7
  • Station Wagon: 0.2

Vehicle is white, probability that it is a:

  • Truck: 0.6
  • Sports Car: 0.1
  • Station Wagon: 0.3

Vehicle has 3 passengers, probability that it is a:

  • Truck: 0.2
  • Sports Car: 0.1
  • Station Wagon: 0.7

If I had info on an unknown vehicle (Has 3 passengers, painted white and is at the golf course) how would I create the combined probabilities that it is each class? How would I do this for n discrete distributions. Are these dependant or independent variables? What is the wording for what I'm trying to do so that I can look it up properly.

Sorry if this is a duplicate question, I don't know the correct jargon for this problem.

$\endgroup$
0
$\begingroup$

I ended up just taking the probabilities for each class and multiplied them together. After that I normalized back to 1. Probably not correct:

Prob that test-car (Has 3 passengers, painted white and is at the golf course) is class x:

  • Truck: (0.1 x 0.6 x 0.2)/Total = 0.012/(0.012+0.007+0.042)
  • Sports Car: (0.7 x 0.1 x 0.1)/Total = 0.007/(0.012+0.007+0.042)
  • Station Wagon: (0.2 x 0.3 x 0.7)/Total = 0.042/(0.012+0.007+0.042)

thus: - Truck: 0.20 - Sports Car: 0.11 - Station Wagon: 0.69

Hope someone comments with a better method than this

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.