uniform distribution in stan/R causes sampling error

Question

I am learning rstan and at the moment I'm solving exercises from Gelmans "Bayesian Data Analysis". For reference this is about the example 5 in chapter 3.

It keeps failing with:

Initialization failed after 100 attempts.  
Try specifying initial values, reducing ranges of constrained values, or reparameterizing the model.
error occurred during calling the sampler; sampling not done

this is my R code:

library(rstan)
scode <- "
transformed data {
  real o_data[5];  
  o_data[1] <- 10;
  o_data[2] <- 10;
  o_data[3] <- 12;
  o_data[4] <- 11;
  o_data[5] <- 9;  
}

parameters {  
  real mu;
  real<lower=0> sigma;
  real tru_val[5];
}

model { 
  mu ~ uniform(0.0,20.0);
  sigma ~ gamma(2,1);
  for (i in 1:5)   {     
    tru_val[i] ~ normal(mu,sigma);
    tru_val[i] ~ uniform(o_data[i]-0.5, o_data[i]+0.5);
  }
}
"

afit <- stan(model_code = scode, verbose=TRUE)

The funny thing is - if I change the second tru_val sampling to tru_val[i] ~ normal(o_data[i],0.5); the model will evaluate just fine.

So far I tried in the stan code:

• rearranging the sampling statements
• introducing helper variables
• explicitely writing increment_log_p statements
• change variable names in case I had accidentially used a keyword
• add print statements in the stan code
• setting mu to 10
• relaxing/widening the constraints in the uniform distribution
• and combinations of above

I noticed something surprising, as I printed the values of tru_val that - no matter which order the statements - I make it prints values around 0 typically between -2 and +2 - even when I set mu <- 10; sigma <- 1; (in the data section) and the sampling statement tru_val[i] ~ uniform(9.5,10.5). I don't really see how it can get these numbers.

I really hope someone can shine some light onto this.

Answer 1

The constraints of the variable need to match the support of the distribution you're using. For tru_val[i] ~ uniform(9.5, 10.5), tru_val has to be defined as real<lower=9.5,upper=10.5> tru_val[5].

In this statement, tru_val[i] ~ normal(mu, sigma), Stan is not drawing a sample from a normal distribution and setting it to tru_val[i]. It is calculating the joint distribution function (in log space); in this case, it's evaluating the normal probability distribution function of tru_val[i] given mu and sigma (in log space).

(The best place to ask questions is on the Stan users mailing list.)