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Bayesian Methods (Basic idea (Calculate p(model/data) for both (ratio of…
Bayesian Methods
Basic idea
allow quantification of strength for the null hypothesis
use prior distributions and probabilities
conditional probabilities
Calculate p(model/data) for both
null model
no effect
alternative model (effect)
ratio of probabilities= bayes factor
3= convincing evidence
=1 No evidence for either
<1 strong odds in favour of the other model
Can set a prior distribution on the effect size
a priori belief as to the probability of the effect size expressed as probability distribution
generally want to set a harsh prior
if curve is steep: high level certainty, if flat, low level
Prior can be based on empirical data
will be more punitive against unexpected effects
requires larger samples etc
conditional probabilities
conditioning probability on the event of something else occurring
not symmetrical
p(a/b) is not equal to p(b/a)
Baye's rule helps to reverse them
P(a/b)= p(b/a)*p(a)/P(b)
a=model b=data
p(data/model)= maximum likelihood maximises
p(model) = the prior
NHST
If you can't reject the null hypothesis
might not have enough power
can't determine whether or not the null hypothesis is true
There are cases where it is necessary to know whether the null hypothesis is true.
=frequentist methods.
deal with long running probabilities
theoretical repetitions of the experiment
