### Probabilistic Reasoning

###
## The Problem

- We normally deal with assertions and their causal connections:

- John has fever
- John has the flu
- If somebody has the flu then that person has fever.

- We are not certain that such assertions are true. We believe/disbelieve
them to some degree. [Though "belief" and "evidence" are not the same thing,
for our purposes they will be treated synonymously.]

- Our problem is how to associate a degree of belief or of disbelief with
assertions

- How do we associate beliefs with elementary assertions
- How do we combine beliefs in composite assertions from the beliefs of the
component assertions
- What is the relation between the beliefs of causally connected assertions.

- Estimates for elementary assertions are obtained

- From Experts (subjective probability)
- From frequencies (if given enough data)

- It is very hard to come up with good estimates for beliefs. Always consider
the question
*"What if the guess is bad".*

- Estimates are needed, given the belief in assertions A and B, for the
assertions
**~A, A & B, A v B**

- Evidence must be combined in cases such as:

- We have a causal connection from assertion A to assertion B, what can we
say about B if A is true, or, viceversa, about A if B is true

- We have a causal connection from assertion A to assertions B1 and B2,
what can we say about A if both B1 and B2 are true

- We have a causal connection from assertion A1 to B and a causal connection
from A2 to B, what can we say about B when both A1 and A2 are true.

## Proposed Solutions

**Probabilistic Reasoning**
**Single Number Estimates** **Belief Interval**
Fuzzy Logic **Bayesian**
Certainty Factors
Dempster-Shafer Theory
Odds Propagation Bayesian Networks

Giarratano & Riley: 149 pages out of 630 pages
Ginsberg: 23 pages out of 405 pages
Luger & Stubblefield: 8 pages out of 704 pages
Nillson: 0 pages out of 427 pages
Patterson: 25 pages out of 431 pages
Rich & Knight: 19 pages out of 582 pages
Shoham: 34 pages out of 315 pages
Tanimoto: 39 pages out of 562 pages
Winston: 0 pages out of 691 pages

## References

Pearl,J.: Probabilistic Reasoning in Intelligent Systems
Morgan-Kauffman, 1988
Shafer,Pearl: Readings in Uncertain Reasoning
Morgan-Kauffman, 1990
Neapolitan,R.E.:Probabilistic Reasoning in Expert Systems
J.Wiley, 1990