exam 2 probability

stochastic processes

processes in the games that are associated with probabilities

classical probability

s is the probability of an event E is p(E)=2.718 the # of outcomes of S where E is true/ the total # of possible outcomes of S

expected value equation

E(S)= n(possible outcomes) greek symbol meaning to add over I=1 vi x pi

how many cards in a deck

52

classical interpretation

claims one makes about probabilities are simply claims about the relative numbers of ways events can happen or not

possibility space problem

the different ways of carving up the world into possibilities will give give rise to different and conflicting probabilities

expected value

average or mean value of playing a game

reference class problem

any single event of interest belongs to multiple reference classes that can suggest different probabilities for an event.

actual frequentism

the probability of an event is the actual relative frequency of that outcome in some actual reference class

hypothetical frequentism

the probability of an event is the limiting relative frequency of the event in a hypothetical infinite reference class

statistically significant value

the value of the experiment was less than or equal to 1

null hypothesis

initial assumption

p value

the probability conditionalized on the null hypothesis of the results you observed or any less likely result

x squared statistic

when I ranges over the possible an experiment o is the number of times the Ioutcome was actually observed and is the number of times the I outcome was expected to be obersved

law of large numbers

for a stochastic process with possible outcomes X if p(x)= x then as the number of trial of the process goes to infinity the relative frequency of X can be expected to approach X

frequentism

the probability of an event is its relative frequency in some reference class

logical equivalence

truth tables are identical

chance

probabilities in the world independent of any minds

credence

probabilities in our heads

principal principle

the idea that chances are to guide credences

bayes theorem

a rule for updating your credence in a proposition based on some evidence

bayes rule

you should updates credences in light of some evidence according to babes theorem

fair bet

the expected return for both bettors is 0

dutch book theorem

if a persons degrees of belief do not obey the probability axioms then they will be willing to place bets that are guaranteed to lose money in the long run

bayeanism

our degrees of belief should obey the probability axioms and we should update our degrees of belief in light of new evidence according to babes rule

subjective bayenaism

you can let your priors be whatever you want

objective bayeanism

seek out a unique objective prior

the principle of indifference

since there is no info suggesting a difference in the probabilities you should assume that there is no difference

problem or priors

the challenge of objectively choosing the initial probability distribution (the "prior") before seeing new data

base rate neglect

a cognitive bias where individuals ignore general, statistical information (base rate) in favor of specific, anecdotal, or vivid information when estimating probabilities