example of truncated data inference, posterior mean vs posterior

data.r

N <- 100
w <- rlnorm(N,0,1)
a <- runif(N,0,1)
m <- 2
keep <- w < a*m
w_kept <- w[keep]
a_kept <- a[keep]
N_kept <- sum(keep)

example.stan

data {
  int<lower=1> N_kept;
  real m;
}
parameters {
  vector<lower=0,upper=1>[N_kept] a_kept;
  vector<lower=0,upper=1>[N_kept] b;
}
model {
  vector[N_kept] w_kept;
  for (i in 1:N_kept) {
    w_kept[i] <- b[i]*a_kept[i]*m;
  }
  increment_log_prob(log(a_kept));
  a_kept ~ uniform(0,1);
  w_kept ~ lognormal(0,1);
}

plot.r

layout(1:2)
posterior_a_kept <- extract(fit_appendix_1,"a_kept")$a_kept
plot(a_kept, colMeans(posterior_a_kept),xlim=c(0,1),ylim=c(0,1))
plot(density(posterior_a_kept), xlim=c(0,1), lwd=2, col="red",
     main="a_kept (data vs posterior)")
hist(a_kept, probability=TRUE, add=TRUE, breaks=10, col="#80ffff60",
     border=NA)
legend("topleft", inset=0.1, col=c("black","#80ffff"), lty=1, lwd=2,
       c("posterior", "data"))