Asymptotic behaviour of the posterior predictive p-value

The posterior predictive p-value is a Bayesian-motivated alternative to the classical concept of p-value. This paper is devoted to study its asymptotic behaviour. Under mild assumptions, it is proved that: a)When θ*, the true value of the parameter, belongs to the null hypothesis, the distribution of the posterior predictive p-value converges to the uniform distribution over the interval (0,1). b)When θ* does not belong to the null hypothesis, the posterior predictive p-value converges almost surely to zero