# tess.PosteriorPredictiveTest: Approximation of the posterior predictive distribution. tess.PosteriorPredictiveTest computes the values of the statistic for the posterior predictive simulations and computes the p-value for the observed statistic. ```r tess.PosteriorPredictiveTest(samples,observation,statistic) ``` ## Arguments - `samples`: Samples from the posterior predictive distribution. - `observation`: The observed value. - `statistic`: The function that computes the statistic. ## Returns Returns a list of the statistic for each sample. ## References S. Hoehna: Fast simulation of reconstructed phylogenies under global, time-dependent birth-death processes. 2013, Bioinformatics, 29:1367-1374 ## Author(s) Sebastian Hoehna ## Examples ```r # We first run an MCMC to obtain samples from the posterior distribution # and then simulate the posterior predictive distribution. # The bird phylogeny as the test data set data(cettiidae) times <- as.numeric( branching.times(cettiidae) ) # The log-likelihood function likelihood <- function(params) { # We use the parameters as diversification rate and turnover rate. # Thus we need to transform first b <- params[1] + params[2] d <- params[2] lnl <- tess.likelihood(times,b,d,samplingProbability=1.0,log=TRUE) return (lnl) } prior_diversification <- function(x) { dexp(x,rate=0.1,log=TRUE) } prior_turnover <- function(x) { dexp(x,rate=0.1,log=TRUE) } priors <- c(prior_diversification,prior_turnover) # Note, the number of iterations and the burnin is too small here # and should be adapted for real analyses samples <- tess.mcmc(likelihood,priors,c(1,0.1),c(TRUE,TRUE),c(0.1,0.1),10,10) tmrca <- max(branching.times(cettiidae)) # The simulation function sim <- function(params) { # We use the parameters as diversification rate and turnover rate. # Thus we need to transform first b <- params[1] + params[2] d <- params[2] # We need trees with at least three tips for the gamma-statistics repeat { tree <- tess.sim.age(n=1,age=tmrca,b,d,samplingProbability=1.0,MRCA=TRUE)[[1]] if (tree$Nnode > 1) break } return (tree) } # simulate trees from the posterior predictive distribution trees <- tess.PosteriorPrediction(sim,samples) # compute the posterior predictive test statistic ppt <- tess.PosteriorPredictiveTest(trees,cettiidae,gammaStat) # get the p-value of the observed test-statistic ppt[[2]] ```

tess.PosteriorPredictiveTest function