Lecture 5

Question 1

bayesian inference =

Answer 1

the outcome of a learning process that is governed by relative predictive success

Question 2

bayesian learning cycle

Answer 2

prior knowledge - prediction - data - prediction error - knowledge update - prior knowledge…

Question 3

wat is theta altijd

Answer 3

hypothesis, something that is unknown and we wish to learn about

Question 4

wat is bayes rule

Answer 4

p(O|data) = P(O) x P(data|O)/P(Data)

posterior beliefs about parameters = prior beliefs about parameters x predictive updating factor

Question 5

uit welke 2 componenten bestaat bayes rule

Answer 5

support en predictive success

Question 6

formule support =

Answer 6

p(O|data) / P(O)

Question 7

formule predictive succes =

Answer 7

p(data|O) / p(data)

Question 8

wat vergelijk je bij support

Answer 8

wat je dacht over theta voordat je de data zag, en wat je nu weet over theta nadat je de data zag.

if the data increased the plausitibility of a value of theta: the data provided support for that value. en zo niet dan minder support

Question 9

wat zie je bij predicitive success

Answer 9

what is the probability of the observed data? how surprising are the observed data vs how surprising are the observed data given a value of theta?

Question 10

wat zegt bayes rule

Answer 10

dat support hetzelfde is als predictive succes

Question 11

wat is surprise in statistics

Answer 11

a bad thing, you want the data to be predictable

Question 12

dus less surprising data =

Answer 12

predictive success, wat betekent dat er support is

Question 13

wat is het verschil tussen support en predicitive success

Answer 13

support = what happens to our beliefs
predictive success = how surprising is our data, how well was our prediction?

Question 14

wat is een ezelsbruggetje

Answer 14

surprise lost is credibility gained.

Question 15

wat is de dotted line

Answer 15

prior distribution on theta
vaak een rechte lijn omdat het makkelijk is, dus alle values are equally likely

Question 16

wat is de niet dotted line

Answer 16

posterior distribution

Question 17

wat zie je als je prior en posterior vergelijkt bijvoorbeeld

Answer 17

dat de waardes onder …. (waar dotted en niet dotted elkaar kruizen) less likely zijn geworden, en waardes die tussen die kruizing liggen zijn meer likely

Question 18

the area under the curve…

Answer 18

needs to be one: dus als een area minder likely is, moet een andere wel meer likely zijn

Question 19

in a continuous distribution, theta can take on any value from …

Answer 19

0 to 1

Question 20

what is the probability in a continuous distribution

Answer 20

not the height, but the area under the curve

Question 21

wat zegt de height

Answer 21

heeft niet echt een interpretatie. maar je kan wel kijken hoe plausibel het a priori was, en dan hoe het a posterior was. de ratio tussen deze twee -> how much more likely is a value in the posterior? dat is de increase in our belief

Question 22

hoe reken je die ratio uit

Answer 22

de bovenste gedeeld door de onderste
posterior / prior

Question 23

p(data) betekenis

Answer 23

probability of the data
if you assume the uniform prior distribution (if any proportion is equally likely a priori) -> then you predict that the number of successes is also uniform. dus alle outcomes are equally likely a priori, if you assume that all values of theta are equally likely a priori. your predictions are very broad

Question 24

if you assume the specific theta (such as 0,50)….

Answer 24

you get much more specific predictions, peaked around bv 0.5.

Question 25

hoe zou je p(O|data)/P(O) kunnen uitleggen

Answer 25

you compare the prior distribution to the posterior distribution, and then we can see how our beliefs have changed.

Question 26

principle parsimony

Answer 26

when you prefer simple over complex explanations, unless the data forces you to abandon the simple explanation

Question 27

posterior belief about theta formule =

Answer 27

p(O|data)

Question 28

prior belief about theta formule =

Answer 28

p(O)

Question 29

change in belief formule =

Answer 29

p(O|data)/p(O)

Question 30

predictive adequacy of theta formule =

Answer 30

p(data|O)

Question 31

average predictive adequacy formule =

Answer 31

p(data)

Question 32

relative predictive adequacy of theta formule =

Answer 32

p(data|O) /p(data)

Question 33

bij wat voor soort distribution weet je meer

Answer 33

bij een peaked distribution, more narrow

Question 34

if the posterior distribution is narrower than the prior distribution, this indicates that the data have ... the uncertainty

Answer 34

reduced

Question 35

ratio a=

Answer 35

the probability of x being lower than [hypothesis], before you have seen the data

Question 36

ratio b=

Answer 36

the probability of x being lower than [hypothesis], after you have seen the data

Question 37

c =

Answer 37

the single most believable number, the highest point, the most likely value

Question 38

d=

Answer 38

hoe veel meer plausibel is value c compared to d (=hypothesis)? ratio d indicates that the value of .... is ... times more probable than the value of [hypothesis]

Question 39

interval e=

Answer 39

a central 95% credible interval which indicates that one can be 95% confident (the posterior probability is 95%) that bobs true iq falls within the interval ranging from ... to ...

Question 40

what does it mean when a model underfits the data

Answer 40

it is too simple. fails to capture the patterns

Question 41

wat is de consensus over variation

Answer 41

variation is random until the contrary is shown

Question 42

simple models tend to make..

Answer 42

precise predictions complex models need to spread out their predictions

Question 43

which model is better supported by the data

Answer 43

the model that predicted the data best

Question 44

posterior beliefs about hypotheses formule =

Answer 44

p(H1|data)/p(H0|data)

Question 45

waarom is de predictive updating factor zo belangrijk

Answer 45

omdat dit het enige is waar mensen het over eens kunnen zijn, de posterior en prior beliefs van iedereen kunnen anders zijn maar we kunnen het er over eens zijn welk model het beter heeft voorspelt

Question 46

dus wat is de predictive updating factor

Answer 46

which model predicted the data the best

Question 47

bf 1-3

Answer 47

anecdotal

Question 48

bf 3-10

Answer 48

moderate

Question 49

bf 10-30

Answer 49

strong

Question 50

bf 30-100

Answer 50

very strong

Question 51

bf >100

Answer 51

extreme

Question 52

4 advantages of the bayes factor

Answer 52

- quantifies evidence instead of forcing an all or nothing decision (kan gewoon zeggen de bayes factor of 3, en dan kunnen mensen zelf interpreteren hoe likely het is) - discriminates 'evidence of absence' from 'absence of evidence' - Allows evidence to be monitored as data accumulate. - Applies to data from the real world, for which no sampling plan can be articulated.

Question 53

evidence of absence =

Answer 53

there is evidence for the null hypothesis, the data is much more likely under the null hypothesis.

Question 54

absence of evidence =

Answer 54

bayes factor near one, there is no evidence. geen significant resultaat zegmaar

Question 55

Allows evidence to be monitored as data accumulate. wat is heir anders dan bij frequentism

Answer 55

frequentism: meer data is ook alpha aanpassen enzo. bij bayes you are simply learning from the data

Question 56

wat is de interpretation van BF01 = 3

Answer 56

the observed data are 3 times more likely under the null hypothesis than the H1

Question 57

dus wat is GEEN goede interpretatie van BF01=3

Answer 57

after seeing the data, h0 is now 3 times more likely than h1. this is only correct when H0 and H1 are equally alike a priori

Question 58

welke error hoor bij die verschillende interpretaties van BF01 = 3

Answer 58

the fallacy of transposing the conditional: Pr(A|B) =/= Pr(B|A)

Question 59

dus wat is de overkoepelende gedachte van bayes factor

Answer 59

the bayes factor quantifies the relative predictive performance. it shows the degree to which the data should shift your opinion. it does not quantify that opinion itself!

Question 60

Every confirmatory instance should increase your confidence in the general law

Answer 60

oke

Question 61

Simple models make daring predictions; if these come true, the simple model is rewarded.

Answer 61

oke

Question 62

if we have n subjects that have successes, what is the bayes factor

Answer 62

n +1