# Selecting statistics for ABC model choice [R code]

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**A**s supplementary material to the ABC paper we just arXived, here is the R code I used to produce the Bayes factor comparisons between summary statistics in the normal versus Laplace example. *( Warning: running the R code takes a while!)*

# ABC model comparison between Laplace and normal nobs=10^4 nsims=100 Niter=10^5 sqrtwo=sqrt(2) probA=probB=matrix(0,nsims,3) dista=distb=rep(0,Niter) pro=c(.001,.01,.1) #A) Simulation from the normal model for (sims in 1:nsims){ tru=rnorm(nobs) #stat=c(mean(tru),median(tru),var(tru)) #stat=c(mean(tru^4),mean(tru^6)) stat=mad(tru) mu=rnorm(Niter,sd=2) for (t in 1:Niter){ #a) normal predictive prop=rnorm(nobs,mean=mu[t]) #pstat=c(mean(prop),median(prop),var(prop)) #pstat=c(mean(prop^4),mean(prop^6)) pstat=mad(prop) dista[t]=sum((pstat-stat)^2) #b) Laplace predictive prop=mu[t]+sample(c(-1,1),nobs,rep=TRUE)*rexp(nobs,rate=sqrtwo) #pstat=c(mean(prop),median(prop),var(prop)) #pstat=c(mean(prop^4),mean(prop^6)) pstat=mad(prop) distb[t]=sum((pstat-stat)^2) } epsi=quantile(c(dista,distb),prob=pro) for (i in 1:3) probA[sims,i]=sum(dista<epsi[i])/(2*Niter*pro[i]) } #B) Simulation from the Laplace model for (sims in 1:nsims){ tru=sample(c(-1,1),nobs,rep=TRUE)*rexp(nobs,rate=sqrtwo) #stat=c(mean(tru),median(tru),var(tru)) stat=mad(tru) mu=rnorm(Niter,sd=2) for (t in 1:Niter){ #a) normal predictive prop=rnorm(nobs,mean=mu[t]) #pstat=c(mean(prop),median(prop),var(prop)) #pstat=c(mean(prop^4),mean(prop^6)) pstat=mad(prop) dista[t]=sum((pstat-stat)^2) #b) Laplace predictive prop=mu[t]+sample(c(-1,1),nobs,rep=TRUE)*rexp(nobs,rate=sqrtwo) #pstat=c(mean(prop),median(prop),var(prop)) #pstat=c(mean(prop^4),mean(prop^6)) pstat=mad(prop) distb[t]=sum((pstat-stat)^2) } epsi=quantile(c(dista,distb),prob=pro) for (i in 1:3) probB[sims,i]=sum(dista<epsi[i])/(2*Niter*pro[i]) }

Filed under: R, Statistics, University life Tagged: ABC, Bayesian model choice, Laplace distribution, R, summary statistics

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