Mon 21 Jun 2010
- In the medical diagnosis, the doctor knows that having a cold causing sneezing.
- Probability that Bob has a cold (unconditionally) P(H) = 0.2
- Probability that Bob sneezes when he has a cold (cond.)
P(E|H) = 0.75
Mathematic
Archived Posts from this Category
Mon 21 Jun 2010
1. All probabilities are between 0 and 1.
0< P(A)< 1
2. True proposition has probability 1.
P(True) = 1
False proposition has probability 0.
P(False) = 0
3. The probability of a disjunction is
P(AvB) = P(A) + P(B) – P(A^B)
Mon 21 Jun 2010
The probability that both events A and B will occur.
- In conditional probabilities, if all we know is about B then P(A|B) is true.
- But when additional information C is available, P(A|B) is no longer valid.
- i.e., we need joint probability of P(A|B^C)
Mon 21 Jun 2010
The posterior probability which is the probability of event A will occur if B occurs or if all we know is about event B.
Conditional probability can be defined in terms of unconditional probabilities.
Mon 21 Jun 2010
A mathematical framework for representing uncertainty about proposition and events.
A random variable is a variable that represents a proposition that can take on values from a set of mutually exclusive values and exhaustive values from the sample space of the random variable.
Mon 21 Jun 2010
A measure that subjects to different background knowledge and experience in evidences.
Mon 21 Jun 2010
A probability expresses a person’s degree of belief in a proposition or the occurrence of an event.
Mon 21 Jun 2010
A probability is measured by a property of a set of similar events such as times of occurring)
Mon 21 Jun 2010
- Frequency interpretation
- Subjective interpretation
- Degrees of belief
- Random variables and distributions
- Unconditional & Conditional Probability
- Joint probability
- The axioms of probability
- Bayes’ rule
- Certainty factor
Mon 21 Jun 2010
Decision Theory
= Probability Theory + Utility Theory
Decision theory uses the principle of Maximum Expected Utility (MEU):
“an agent is rational if it chooses the action that yields the highest expected utility, average over all the possible outcomes of the action.”