# Bayesian stats: trick to accept the null?

There's a lot to be said and read about this, but I haven't found a clear answer to this question:

Bayesian statistics are said to 'penalize' vague hypotheses with weak priors, by giving more support for the null hypothesis.
Say the theory I'm interested in proving actually predicts that the null is true. I could cheat, and set up my model with a weak prior. This would unfairly bias my empirical evidence towards the null. How can this be prevented?

Thanks!

EDIT: I realized I was actually referring to Lindley's paradox, where as far as I understand) a precise null and an uninformative prior might bias towards the null, whereas frequentist statistics would reject the null. http://www.laeuferpaar.de/Papers/LindleyPSA.pdf

• What is your null hypothesis ? Something like $H_0\colon\{\theta=\theta_0\}$ ? – Stéphane Laurent Jul 22 '14 at 7:47
• Yes, something like this. – elisa Jul 22 '14 at 8:22
• Reference intrinsic inference is a formal answer to such kind of problem. See this example and references given therein. – Stéphane Laurent Jul 22 '14 at 8:26
• What is a "vague" hypothesis by the way ? $H_0\colon\{\theta=\theta_0\}$ doesn't sound vague for me. – Stéphane Laurent Jul 22 '14 at 8:34
• I have just taken a look at Sprenger's paper mentionned in your edit. The Bayesian reference criterion (BRC) is more or less what I called "reference intrinsic inference" in my previous comment. – Stéphane Laurent Jul 22 '14 at 8:37