Page 115 - DCAP506_ARTIFICIAL_INTELLIGENCE

Unit 8: Statistical Reasoning

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

P(E|H )P(H )
 Bayes Theorem, that is P(H |E)  i i signifies that specified some
i n
 k 1 P(E|H )P(H )
k
k

evidence E then probability that hypothesis is true is equal to the proportion of the
probability that E will be true specified H times the a priori evidence on the probability
i
of H and the sum of the probability of E over the set of all hypotheses times the probability
i
of these hypotheses.
 Bayesian statistics lounge at the heart of many statistical reasoning systems.
 Bayesian networks are also known as Belief Networks or Probabilistic Inference Networks
primarily generated by Pearl (1988).
 Certainty Factors do hold on to the rules of Bayesian statistics, but it can symbolize
tractable knowledge systems.
 Fuzzy logic concentrates on ambiguities in illustrating events rather than uncertainty
regarding the incidence of an event.
 Fuzzy set theory defines set membership as a possibility distribution.

8.6 Keywords

Bayesian networks: Bayesian networks are also known as Belief Networks or Probabilistic
Inference Networks primarily generated by Pearl (1988).
Fuzzy Logic: Fuzzy logic concentrates on ambiguities in illustrating events rather than uncertainty
regarding the incidence of an event.
Fuzzy Set: Fuzzy set theory defines set membership as a possibility distribution.
Probabilities: Probabilities are (real) numbers in the range 0 to 1.

8.7 Review Questions

1. What is Bayes Theorem? Also illustrate Bayes rule-based systems.

2. Enlighten the probabilistic reasoning aspects of MYCIN.
3. Given that the first card dealt from a pack of cards was ace what is the probability that the
next card will be an ace?

4. What are Bayesian networks? Illustrate the concept of implementation with example.
5. Given that
(a) the probability that it will rain in Cardiff tomorrow is 0.8

(b) the probability that there are Sea Gulls on Roath Park lake given that it will rain
tomorrow is 0.1
(c) the probability that there are Sea Gulls on Roath Park lake given that it will not rain
tomorrow is 0.05
What is the probability that it will rain tomorrow provided that there a Sea Gulls on Roath
Park lake?

LOVELY PROFESSIONAL UNIVERSITY 109