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Bayesian statistics

Q: What are advantages for bayesian statistics compared to frequentist statistics?

P values do not give evidence for H0 regardless of whether power is high or low. The bayes factor does have the ability to give evidence for H0 P values do not provide evidence for H1 in ways sensitive to properties of H1: P values do not punish theories for being vague, bayesian statistics do this. bayes factorsprovide a continuous measure of evidence based on the data, knowledge can continuously get updated.

5 important questions on Bayesian statistics

What is necessary to perform bayesian statistics?

Data
a generative model
priors; what information the model has before seeing the data

also, every parameter in the model has to be quantified in probability

What is bayesian inference?

A generative model can be used to feed parameter values and generate data.
often we are in the opposite situation; the data is known
in bayesian inference you want to use the generative model to see what parameter values can give rise to the found data.

What are ways to summarize the posterior probability distribution?

the maximum likelihood estimate is the parameter value that is most likely to result in our found data.
the posterior mean is the mean parameter values that is most likely to result in our found data.
a x% credible interval; the chance of the parameter being between these two boundaries is x%

How can you use the bayes factor to interpret data?

A bayes factor of 1 indicates that the experiment did not provide any evidence towards h0 or h1
a bayes factor >1 indicates that the data provides evidence for h1
a bayes factor <1 indicates that the data provides evidence for h0

a bayes factor of larger than three or smaller than 0.3 can be considered significant evidence

What are advantages for bayesian statistics compared to frequentist statistics?

P values do not give evidence for H0 regardless of whether power is high or low. The bayes factor does have the ability to give evidence for H0
P values do not provide evidence for H1 in ways sensitive to properties of H1: P values do not punish theories for being vague, bayesian statistics do this.
bayes factorsprovide a continuous measure of evidence based on the data, knowledge can continuously get updated.