2- Information and Uncertainty Flashcards
What is an outcome space (Ω)?
The set of all possible individual outcomes Ω={A1,…An}
What is the OR axiom?
If A and B are mutually exclusive, the probability of A or B is the sum of the two P(A∪B)=P(A)+P(B)
What is the AND rule?
If A and B are independent, the probability of A and B is the product of the two P(A∩B)=P(A)xP(B)
What is the conditional probability formula?
P(A|B) = P(A∩B)/P(B)
What is the General AND rule?
P(A∩B) = P(A|B)xP(B)
What are 2 ways of proving independence?
- P(A|B)=P(A)
- P(A∩B)=P(A)xP(B)
What is the rule of total probability?
P(A)=[P(A|B)xP(B)]+[P(A|¬B)xP(¬B)]
What is Bayes’ rule?
P(A|B) = [P(B|A)xP(A)]/P(B)
What is Prior probability in Bayesian updating?
The probability that a hypothesis is true P(H) before evidence E is revealed
What is Posterior probability in Bayesian updating?
The probability that a hypothesis H is true given evidence E is revealed P(H|E)
What is the Bayesian updating formula for posterior probability?
P(H|E) = [P(E|H)xP(H)]/[P(E|H)xP(H)+P(E|¬H)xP(¬H)]
What is the Gambler’s fallacy?
Belief, that a departure from the average behaviour of some (random) system will be corrected in the short term
What is the conjunction fallacy?
The false belief that 2 events occurring is more likely than one of those events occurring
What is the disjunction fallacy?
Underestimating the probability of a disjunction e.g. feminist bank clerk
What is the base-rate?
The fraction of some population that has some characteristic of interest
What is base-rate neglect?
The failure to take the base rate properly into account in probabilistic judgement
What is Confirmation bias?
The tendency of individuals to interpret evidence as supporting prior beliefs to a greater extent than warranted
What is the Availability heuristic?
Assessing the probability of an event based on the ease/availability with which the event comes to mind
What is Overconfidence?
Subjects’ confidence in their probability judgements exceed the frequency with which those judgements are correct
When is a test non-diagnostic?
When the conditional probability is close to the base rate P(A|B)≈P(A)
