Beyes III Flashcards
bayesian inference and bayesian hypothesis testing difference
bayesian inference is based on parameter, bayesian hypothesis testing is based on the hypothesis
marginal likelihood in hypothesis testing
bovenaan, gaat over H1
likelihood in hypothesis testing
onderaan, gaat over H0
hoe zie je of iets one sided of two sided is?
straight line = two sided!!!
als het opeens omhoog gaat = one sided!!!
parsimony
the specific predictions, when still accurate, get rewarded more!
how do you choose the prior distribution
baseren op knowledge of previous studies or keep informative
what is the same about the prior distribution and the parameter
it needs to be in the same domain!
which domains are there?
proportion: [0,1]
correlation: [-1,1]
difference in means: [-∞, ∞]
wat meet je bij een bayesian correlation
rho (p)
wat meet je bij een bayesian proportion
theta θ
3 vormen van Ha
H1: p =/= 0
H+: p > 0
H-: p< 0
dus als je een rho ziet, welk domein is dat dan
correlation: -1 tot 1
-> stretched beta distribution
hoe kan je de median krijgen
median = top van grafiek.
meaning that there is a 50% that rho is equal to or lower than the observed correlation
95% credible interval
95% probability that ρ is between … and …, under this model
larger sample size leads to
more narrow likelihood, posterior distribution and credible interval
-> we can make a more specific prediction (with a higher BF), with the same certainty
δ =
delta, cohens d.
staat voor differences between groups
wat meet je bij een bayesian t test
the differences between groups, delta
welk domein is een t test
difference in means: dus [-∞, ∞]!
welke distribution gebruik je bij dit domein: [-∞, ∞]
Cauchy distribution, (= t distribution) with df = 1
(a uniform distribution would not work, because the domain is infinite)
The Cauchy distribution is governed by a single shape parameter
that determines how wide it is
oke
what is the “uninformative distribution” for the t test (difference in means)
width of 0,707:
50% of the values of delta are within -0,707 and 0,707
bayes robustness check
= sensitivity analysis: what would have happened if we chose a different value for the prior width?
je ziet dan een grafiek met alle possible values voor de width. als die recht is, dan zat er niet zoveel verschil tussen de mogelijke waardes
Bayes vs. frequentism
Frequentist Hypothesis
testing
1) Specify alpha x
2)Assumptions
3) Hypothesis
4) Test statistic + sampling x
distribution
5) P-value x
6) Conclusion
Bayesian Hypothesis testing
1) Assumptions
2) Hypothesis
3) Set prior distribution x
4) Compute likelihood x
5) Bayes factor x
6) Conclusion
doel van Bayes
compare the predictive quality of two models/hypotheses
doel van frequentism
minimize type 1 error (falsily rejecting H0)
hoevaak kijken beiden technieken naar de data
Bayes: meerdere keren, updaten
Frequentism: maar 1 keer kijken (want meerdere keren = grotere kans op type 1 error)
beide methoden kijken naar…
assumpties
welke is meer compleet van de methoden
frequentism
verschillen in sampling plans tussen de methoden
- bayes: can keep on monitoring sampling plan, update when needed and stop when preferred
- frequentism: need to specifiy beforehand and you cannot deviate from it
– ‘evidence for HA’
– ‘probability that H0 is true’
incorrect!!!
wat is de definitie van de p waarde
‘The probability of these data or more extreme if H0 is true’
“Absence of evidence” vs “evidence of absence”
absence of evidence: je kan niets bewijzen
evidence of absence: het effect is er gewoon niet
preregistration
Before you conduct your study, you preregister several pieces of information:
Description of study, sampling plan
Hypotheses (+ one-sided/two-sided)
What statistical tests, and what settings: prior and Bayes factor / alpha-level for
accepting or rejecting hypothesis
exploratory research
generate theories and hypotheses
confirmatory research
test those theories and hypotheses from exploratory research
what do journals do to promote preregistration
Registered reports:
Write most of your paper+preregistration, without conclusions, when it gets
accepted by the journal you conduct the experiment fill in the results and conclusion
section of your paper based on the results
Increased support for null findings
robustness check/sensitivity analysis
check the effect of the prior on the Bayes factor
the BF is…
relative!!!
Bayes does not fix all your problems: equally vulnerable to
assumption violations and statistical malpractice!
oke
what 2 things can help with bettering science
- preregistration
- open science
verschil sampling distribution and posterior distribution
- sampling: what would happen if we repeat over and over
- posterior: how well do all the values of the parameters predict the data? (prior + likelihood = posterior)
verschil confidence interval and credible interval
- confidence interval: if we repeated this over and over, x% of the intervals would contain the true value
- credible interval: x% probability that this interval contains the true value