1. Bayesian ARgumentation via Delphi — BARD
Erik Nyberg, Kevin Korb, Ann Nicholson, Steven Mascaro
ABNMS 2017
University of Melbourne
Korb BARD

2. BARD
Blue and Green Cabs
Agatha's Auction
Artful Deception
Korb BARD

3. Blue and Green Cabs
It was a dark & stormy night. A cab was involved in a hit and run accident. Two cab companies, the Green and the Blue, operate in the city. 85% of the cabs in the city are Green and 15% are Blue. A witness identified the cab as Blue. The court tested the reliability of the witness under similar circumstances and found that the witness correctly identified each one of the two colors 80% of the time and failed 20% of the time. Question: What is the probability that the cab involved in the accident was Blue?
Korb BARD

4. Blue and Green Cabs
P(B) = .15 P("B"|B) = .8 P("B"| −B) = .2 P(B|"B") = P("B"|B) P(B) ÷ (P("B"|B) P(B) + P("B"|−B) P(−B) = .8 x .15 ÷ (.8 x x .85) = .12 ÷ ( ) ≈ .41
Korb BARD

5. Blue and Green Cabs
Blue ↓
"Blue"
Korb BARD

6. Agatha's Auction House
Question: What are the chances that a purchased painting is an original?
Facts ("Key Elements"):
Agatha's sells both originals and reproductions
Painting sold as original
Shipping docs reveal 40% sold as original, 60% as repro
Expert declares it's original
Expert under test gets it right 80% of time (TP and TN)
Korb BARD

7. Agatha's Auction Despite being "modeled on" Green/Blue Cabs
What's missing just is the base rate:
the probability that a painting is original
"Shipping docs reveal 40% sold as original, 60% as repro" was confused with this
Confusing "sold as" with "being" original
Building a BN reveals what is missing
Korb BARD

8. Artful Deception
BARD members sought to fix "Agatha's Auction" producing "Artful Deception". Facts ("Key Elements"):
Agatha's sells both originals and reproductions
Painting sold as original
Warehouse contains 20% originals, 80% as repro
Expert declares it's original
Expert under test gets it right 70% of time (TP and TN)
The two node network suffices, even though there is a third node "Sold as original" whose likelihoods are not given in the story.
Korb BARD

9. Artful Deception
The answer btw is: P(O) = .2 P("O"|O) = .7 P("O"| −O) = .3 P(O|"O") = P("O"|O) P(O) ÷ (P("O"|O) P(O) + P("O"|−O) P(−O) = .7 x .2 ÷ (.7 x x .8) = .14 ÷ ( ) ≈ .37
Korb BARD

10. Solution: The BARD
Korb BARD