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2 Example Model and Data

The following is a simple, complete Stan program for a Bernoulli model of binary data.² The model assumes the binary observed data y[1],...,y[N] are i.i.d. with Bernoulli chance-of-success theta.

data { 
  int<lower=0> N; 
  int<lower=0,upper=1> y[N];
} 
parameters {
  real<lower=0,upper=1> theta;
} 
model {
  theta ~ beta(1,1);  // uniform prior on interval 0,1
  y ~ bernoulli(theta);
}

The input data file contains definitions for the two variables N and y which are specified in the data block of program bernoulli.stan (above).

A data set of N=10 observations is included in the example Bernoulli model directory in both JSON notation and Rdump data format where 8 out of 10 trials had outcome 0 (failure) and 2 trials had outcome 1 (success). In JSON, this data is:

{
    "N" : 10,
    "y" : [0,1,0,0,0,0,0,0,0,1]
}

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2. The model is available with the CmdStan distribution at the path <cmdstan-home>/examples/bernoulli/bernoulli.stan.↩