alt Hacker NewsThe evidence "actually supports the null" over what alternative?
In a Bayesian analysis, the result of an inference, e.g. about the fairness of a coin as in Lindley's paradox, depends completely on the distribution of the alternative specified in the analysis. The frequentist analysis, for better and worse, doesn't need to specify a distribution for the alternative.
The classic Lindley's paradox uses a uniform alternative, but there is no justification for this at all. It's not as though a coin is either perfectly fair or has a totally random heads probability. A realistic bias will be subtle and the prior should reflect that. Something like this is often true of real-world applicaitons too.
Thank you. The main problem with Bayesian statistics is that if the outcome depends on your priors, your priors, not the data determine the outcome.
Bayesian supporters often like to say they are just using more information by coding them in priors, but if they had data to support their priors, they are frequentists.