Page 107 - DCAP506_ARTIFICIAL_INTELLIGENCE

Unit 8: Statistical Reasoning

if the number of exceptions is huge such system is apt to break down many common sense and Notes
expert reasoning tasks for instance. Statistical techniques can summarize huge exceptions without
resorting enumeration.

8.1 Probability and Bayes Theorem

8.1.1 Probability

The fundamental approach statistical methods approve to deal with uncertainty is through the
axioms of probability:

 Probabilities are (real) numbers in the range 0 to 1.
 A probability of P(A) = 0 symbolizes total uncertainty in A, P(A) = 1 total certainty and
values in among some degree of (un)certainty.

 Probabilities can be computed in a number of manners.
Probability = (number of desired outcomes)/(total number of outcomes)
So specified a pack of playing cards the probability of being dealt an ace from a full usual deck
is 4 (the number of aces)/52 (number of cards in deck) which is 1/13. Likewise the likelihood of
being dealt a spade suit is 13/52 = 1/4.

n!
n
If you have a option of number of items k from a set of items n then the C  formula
k
k!(n k)

is applied to discover the number of methods of making this option. (! = factorial).
49!
Thus the possibility of winning the national lottery (choosing 6 from 49) is = 13,983,816
6!43!
to 1.

Notes Conditional probability, P(A|B), signifies the probability of event A specified that
we know event B has appeared.

Task Illustrate the concept of probability.

8.1.2 Bayes Theorem

This specifies:

P(E|H )P(H )
P(H /E)  n i i
i
 k 1 P(E|H )P(H )
k
k

This signifies that specified some evidence E then probability that hypothesis H is true is equal
i
to the proportion of the probability that E will be true specified H times the a priori evidence on
i
the probability of H and the sum of the probability of E over the set of all hypotheses times the
i
probability of these hypotheses.

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