Probability Flashcards
(49 cards)
What is the difference between deductive and inductive logics?
In deductive logic the conclusion follows from the premises with certainty i.e. the logic condition is fulfilled and no risk is involved;
In inductive logic the conclusion only follows with some probability, making it a risky inference. The conclusion bears some risk of not following with certainty from valid premises.
Deductive logic is valid only with certainty while inductive is valid if the conclusion is strong.
What does the 3 point triangle mean in logics and mathematics?
Therefore
Which two questions must be answered before an inductive argument can be properly evaluated?
- How strong in the inference from the premises to the conclusion (what’s is the probability that the conclusion is true, given the premises)?
- How high does the probability have do be before it is rational to accept the conclusion
(What the rational threshold)?
What is the range of a probability function P(A) where P is the probability and A is an event.
Between 0 and 1 (0% chance and 100% chance)
Given P(A) and P(B), what does probability theory give us?
It gives us the rules for calculating, among others:
P(not-A);
P(A and B);
P(A or B);
P(A given B).
This is probability calculus.
In the classical interpretation, given a random trial with a set of possible outcomes, what is P(A)?
Number of favourable cases (that give A)
Divided by
Total number of equally possible cases.
What is the principle of indifference?
We should treat a set of outcomes as equally possible if we have no reason to consider one outcome more probable than the other (or others).
When does the principle of indifference apply?
When we have no evidence at all;
When we have symmetrically balanced evidence.
What are the shortcomings of the classical interpretation of probability?
Finite number of elementary outcomes;
Equal possibility for each elementary outcome.
Is the classical interpretation of probability good enough as a theory?
No, it’s especially good for gambling only.
Define the logical probability interpretation of probability.
The degree of logical support that a conclusion has, relative to a set of premises;
i.e.
The degree of confirmation that evidence confers on a hypothesis.
What is the frequency theory of probability?
E
What is finite relative frequency?
When the number of trials is certain and finite. It deals with a finite number of observed trials.
What is a limiting relative frequency?
When we are asked to consider what the relative frequency would converge to in the long run if we had an infinite number of trials.
What are the shortcomings of frequency interpretation of probability.
We cannot know wage will happen in the infinite time frame.
Not suitable for single-case events.
What is the Bayesian (subjective) theory of probability?
A theory that states that probability is subjective to the observer. It tries to assign a number to a persons degree of belief.
What is a Dutch book contract?
A bet that is a guaranteed loss (sure-loss contract).
What is the basic rule of Bayesian rationality?
No rational person will willingly agreed to a bet that is a sure-loss.
What name is given to set of personal beliefs that is not open to a Dutch book contract?
Coherent
What does Bayesian probability used for?
What is the basic Bayes’ rule?
Explain each variable and component of the equation.
Normally used to asses the probability of an hypothesis given the evidence - P(H/E).
P(H/E)=(P(H)*P(E/H))/P(E)
H=hypothesis
E=evidence
Where P(H/E) is the posterior probability of H;
P(H) is the prior probability of H;
P(E/H) is the likelihood of the evidence E if H is true;
P(E) is the total probability of E.
What is epistemic probability?
Give examples.
Is the probability of an event GIVEN certain evidence.
It is based on the evidence available (what we know).
Examples: Logical probability and Bayesian probability interpretations.
What is objective (physical) probability?
Give examples.
Probability that depends on objective features of nature (the world) that were discovered and not subject to belief disputes.
Examples: classical, frequency-based and propensity interpretations of probability.
What is the propensity theory of probability?
A theory that proposes that the long-term (limit) value of the probability of an event depends on propensities peculiar to individual events.
What are the two languages used to refer to probability?
Propositional languages; and
Event language
