Week 6 SCM (Bayes)

Question 1

what is bayesian statistics vs. frequentist statistics

Answer 1

• bayesian is a way of understanding data based on the odds of various outcomes
• the frequentist approach looks at the probability of different data under the null hypothesis (pvalues).

Question 2

what is a latent process?

Answer 2

the name given to an unseen (random) process that generates observed data

Question 3

what is a latent variable?

Answer 3

a variable that is not observed but rather inferred through a mathematical process

for example a population mean can be a latent variable that is inferred through the sampling of a population and analysis of the sample mean

Question 4

what is bayesian inference?

Answer 4

the process of making inferences about a latent variable based on observed data, e.g estimating a population mean from the sample mean

Question 5

how to estimate posterior distribution using bayesian inferences

Answer 5

• if we dont have specific information for the prior we can use a distribution as the prior such as a uniform distribution
• these priors can be uninformative or weakly informative
• its implies that all values are equally likely

Question 6

what is the MAP (maximum a posterieori) estimate?

Answer 6

• the value in the distribution in which the probability is the highest

Question 7

what does a 95% credible interval tell us?

Answer 7

• there is a 95% probability that the probability value of an outcome falls between these two values
• it can be used to show that the probability of an outcome is significantly above 0 suggesting that the outcome is likely to happen

Question 8

how is it common to generate credible intervals?

Answer 8

by sampling from the posterior distribution and then computing quantiles from the samples

Question 9

whats the bayes factor?

Answer 9

the bayes factor characterises the relative likelyhood of the data under two different hypothesis’s

Question 10

what is the hypothesis test for the frequentist and bayesian approaches?

Answer 10

Frequentist test= p values

Bayesian= Bayes Factor

Question 11

What is the estimation of uncertainty for the frequentist and bayesian approaches

Answer 11

Frequentist= maximum likelyhood estimate with confidence intervals

Bayesian= posterior distribution with highest density interval

Question 12

where is the marginal likelyhood in the bayes formula

Answer 12

the marginal likelyhood is on the denominator of the equation

(the numerator of the equation includes the prior and the likelyhood)

Question 13

what is the bayes factor formula

Answer 13

BF= P (data | H1) / P (data | H2)

Question 14

how do you interpret bayes factors

Answer 14

> 150 is very strong significance
20-150 is strong
3-20 is positive
1-3 is not really worth a mention

Question 15

why is the bayes factor better for assesing evidence for the null hypothesis

Answer 15

• because the bayes factor is comparing evidence for the two hypotheses it allows us to assess whether theres evidence for the two hypotheses
• we cant do this with standard null hypothesis testing because it starts with the assumption that the null is true

Question 16

what is it called if two vectors have the same orientation but only differ in length?

Answer 16

they are called linearly dependent

Question 17

when would two vectors be orthogonal?

Answer 17

if theyre inner product equals zero

therefore the scalar between the two vectors must not equal zero

Question 18

are orthogonal vectors and uncorrelated vectors dependent or independent

Answer 18

all orthogonal and uncorrelated vectors are independent

Question 19

whats a nonequivalent control group design

Answer 19

uses prexisting groups, one of which serves in the treatment condition and the other in the control condition

Question 20

whats a posttest only nonequivalent control group design

Answer 20

compares two prexisting groups
one is measured after a treatment and the other is measured at the same time but recieves no treatment

the pretestpostest nonequivalent control group design is much better

Question 21

whats a pre post design?

Answer 21

when a series of observations is made over time for one group of participants

Question 22

what is a time series design

Answer 22

like a treatment design except there is an event not a treatment
this event is not controlled by the researcher