1.
Artificial Intelligence
Version 1.0
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2.
Two gambles
we bet on a head turning up when we toss a coin that is
known to be fair
we bet on the outcome of a fight between the world's
greatest boxer and the world's greatest wrestler.
2RS, CSE@KUET
3.
Why DST
If we have absolutely no information about the coin, in
probability theory,
we will assume that it would be 50% head and 50% tail
we know the coin is fair, so we know for a fact that
it would be 50% head and 50% tail.
Therefore, in the two different scenarios,
we arrive at the same conclusion.
How we present total ignorance in probability theory
becomes a problem.
3RS, CSE@KUET
4.
Why DST
In Dempster–Shafer Theory,
for the ignorance scenario,
the belief of Head and the belief of Tail would be 0.
For the fair coin scenario,
the belief of Head would be 0.5, the belief of Tail would also
be 0.5.
4RS, CSE@KUET
8.
Effects of conflict (Low Conflict)
Suppose that one doctor believes a patient has
either a brain tumor — with a probability of 0.99
or meningitis — with a probability of only 0.01.
A second doctor also believes the patient has
a brain tumor — with a probability of 0.99
and believes the patient suffers from concussion — with
a probability of only 0.01.
If we calculate m (brain tumor) with Dempster’s
rule, we obtain m(brain tumor)=Bel (brain tumor)=1
8RS, CSE@KUET
9.
Effects of conflict (High Conflict)
Suppose that one doctor believes
a patient has either meningitis with a probability of
0.99
or a brain tumor with a probability of only 0.01.
A second doctor believes
the patient suffers from concussion with a probability of
0.99
and also believes the patient has a brain tumor with a
probability of only 0.01.
If we calculate m (brain tumor) with Dempster’s
rule, we obtain m(brain tumor)=Bel (brain tumor)=1
9RS, CSE@KUET
10.
Belief and Plausibility
Shafer's framework allows for belief about propositions
to be represented as intervals, bounded by two
values, belief (or support) and plausibility:
belief ≤ plausibility.
10RS, CSE@KUET
11.
Belief and Plausibility
Suppose we have a belief of 0.5 and a plausibility of 0.8
for a proposition, say “the cat in the box is dead.” This
means that we have evidence that allows us to state
strongly that the proposition is true with a confidence
of 0.5. However, the evidence contrary to that
hypothesis (i.e. “the cat is alive”) only has a confidence
of 0.2. The remaining mass of 0.3 (the gap between the
0.5 supporting evidence on the one hand, and the 0.2
contrary evidence on the other) is “indeterminate,”
11RS, CSE@KUET
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