Bayes inference: hypothesis testing on the average parameter Bayesian inference field: given a dataset, if I assume a normal a priori distribution on the average parameter with zero mean and a given variance, those hypothesis tests can be carried out on the posterior distribution to assume (with a certain confidence level) that is the average really zero? Does it make sense to apply the t-test statistic on a posterior distributions (t.test in R) or is the t-test an exclusive hypothesis test of the sample media?
 A: It does not make sense to apply a t-test on a posterior distribution - a t-test is applied to do data (although you could represent a prior through pseudo observations and then do a frequentist analysis such as a t-test). 
One would more typically do one of the following:


*

*look at how much posterior mass there is on the parameter being exactly zero (with a normal prior that would be zero, but you could create a point mass at zero in your prior - but see Lindley's paradox - or you could look at the posterior mass in an interval around zero that includes values that are in practical terms more or less zero)

*Bayesian model averaging between models with the parameter set to zero vs. not set to zero

*look at posterior credible intervals for the parameter (do they include zero and exclude values that are meaningfully different from zero?)

*look at the Bayes factor between a model with the parameter to be estimated versus the parameter fixed at zero
Which of these makes the most sense may depend on what you are trying to do. 
