lecture 8 (2)

Question 1

Frequency interpretation of probability

Answer 1

the probability of an outcome is the frequency with which the outcome occurs in a long sequence of trials

NOTE: Frequentism is associated with scientific tools such as NHST maximum likelihood estimation, p values

Question 2

What is a long sequence of trials

Answer 2

similar to an experiment repeated over and over to produce an infinite series of observations about the value of a variable of interest

E.g. I want to find the probability of the outcome heads for a given coin. Thus, I flip the coin, record the outcome, and repeat over and over. In the limit, the relative frequency of the outcome heads gives me the probability of the outcome heads

Question 3

One problem frequency interpretation

Answer 3

ON the frequency interpretation, it is hard to tell how we should assign probabilities to one off events that do not repeat themselves

E.g. on a frequentist interpretation, one cannot tell the probability that humans will land on venus by 2025 or that willhelm 2 will win the leage this year

Question 4

Propensity interpretation of probability

Answer 4

The probability of an outcome is a propensity inherent in the physical conditions producing the outcome

Question 5

Propensity can be understood as

Answer 5

causal disposition of a situation to produce certain outcomes

Question 6

causal disposition

Answer 6

A tendency to behave in a certain way under certain circumstances

E.g. Being fragile is a causal disposition of glass. It is the tendency of glass to break when dropped

Question 7

One problem of propensity interpretation

Answer 7

it is hard to tell how we should assign some conditional properties, because probabilities are invertible but causal tendencies are not invertible

E.g.

The probability of the outcome red card given that you draw an ace is PROB(Colour = red I Card = ace) = 2/$

The probability of hte outcome ace given that you draw a red card is

Prob(Card = ace I colour = red) = 2/26

but causes are not invertible

E.g. the approaching rain made the weather alarm on my phone beep. Rain&raquo_space; weather alamr

The weather alarm on my phones beeping cuased rain approaching

Weather alarm&raquo_space;» rain (stoopid)

so if propensities are causal tendencies, they cannot easily capture the invertibility of conditional probability