Dear Friends, According to Gelman et al (2003), "...Bayesian P-values are defined as the probability that the replicated data could be more extreme than the observed data, as measured by the test quantity p=pr[T(y_rep,tetha) >= T(y,tetha)|y]..." where p=Bayesian P-value, T=test statistics, y_rep=data from replicated experiment, y=data from original experiment, tetha=the function of interest. My question is, How do I calculate p (the bayesian P-value) in R from the chain I obtained from the Gibbs sampler? I have a matrix 'samp' [10,000x86] where I stored the result of each of the 10,000 iterations of the 86 variables of interest. Something I want to add is that Gelman also states that "...in practice, we usually compute the posterior predictive distribution using simulation. If we already have L simulations from the posterior density of theta, we just draw one y_rep from the predictive distribution for each simulated theta; we now have L draws from the joint posterior distribution, p(y_rep,theta|y). The posterior predictive check is the compariosn between the realized test quantities, T(y, theta_L) ant the predictive test quantities, T(y_rep, theta_L). The estimated P-value is just the proportion of these L simulations for which the test quantity equals or exceeds its realized value; that is, for which T(y_rep,theta_L)>=T(y,theta_L)..." Does this means that the usual p-value applies? i.e., pv <- 1 - chosen_CDF(parameters)? Can anybody clarify that for me please? Thanks for your help. Jorge
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