You know some investigators want to cancel the p-value as a statistical parameter. And some of them suggest Bayes statistics. Can you show how it will work on a simple example? E.g. I want to compare the two groups. I can use chi2 with a p-value for now, but how can I use Bayes statistics in this case?
This is a wide open question! To start at the back end, look here. But there is much to the front end. Look at these resources: Introduction to Bayes for Evaluating Treatments - 12 Resources.
Briefly, you can choose a Bayesian model that is similar to the frequentist data model, e.g., for comparing two probabilities \theta_{1}, \theta_{2}. Then you can arrive at \Pr(\theta_{1} < \theta_{2} | \mathrm{data}) under a certain prior distribution. For comparing two proportions as in a Pearson \chi^2 test, it is useful to think of this as a Bayesian binary logistic regression model where you have a flat prior on the intercept and a normal distribution prior for the slope (difference in log odds of outcomes between the two groups).
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somewhere on this message board a weblink was given providing a bayesian re-analysis of a clinical trial. it might be instructive, if i could find it …