Hi,

I’m learning Bayesian statistics using “A Student’s Guide to Bayesian Statistics by Ben Lambert”. I’m working through an example in the later chapters of the book where the aim is to infer how many times a coin was flipped `N`

given that 10 experiments were performed and the number of heads in each experiment is given by the data in `Y`

below.

The code below is copied from the book and compiles without errors but when I try and fit the code I get a runtime Initialization error (see separate Python and Stan(terminal) traces at the bottom of post). I think I understand why the error appears but I’m not sure how to fix it. I’ve tried changing things the “transformed parameters” section of the Stan model code, particularly playing with the `(Y | N[s], theta)`

portion of the `binomial_lpmf`

by removing and adding `[s]`

from the code but the error is pretty much always the same even though some of the numbers may change. Any help with this would be greatly appreciated.

Many thanks,

Jaf

p.s. apologies if I’ve missed any standards for this forum - it’s my first post.

```
Y = [9,7,11,19,19,9,8,11,9,11]
nStudy = 10
model_code = """
data {
int nStudy;
int Y[nStudy];
}
transformed data{
int N[10];
for (s in 1:10)
N[s] = 10 + s;
}
parameters {
real<lower=0,upper=1> theta;
}
transformed parameters {
vector[10] lp;
for (s in 1:10)
lp[s] = log(0.1) + binomial_lpmf(Y | N[s], theta);
}
model {
target += log_sum_exp(lp);
theta ~ beta(7,2);
}
generated quantities {
simplex[10] pState;
pState = exp(lp - log_sum_exp(lp));
}
"""
sm = StanModel(model_code=model_code)
fit = sm.sampling(
data=dict(nStudy=nStudy,Y=Y),
warmup=500,
iter=1000,
chains=4,
seed=1
)
```

PYTHON ERROR TRACE:

```
---------------------------------------------------------------------------
RemoteTraceback Traceback (most recent call last)
RemoteTraceback:
"""
Traceback (most recent call last):
File "/home/jaf/.conda/envs/pystan-env/lib/python3.8/multiprocessing/pool.py", line 125, in worker
result = (True, func(*args, **kwds))
File "/home/jaf/.conda/envs/pystan-env/lib/python3.8/multiprocessing/pool.py", line 48, in mapstar
return list(map(*args))
File "stanfit4anon_model_39368d80adc693f1938ef1ee0051a427_1056900776692445796.pyx", line 373, in stanfit4anon_model_39368d80adc693f1938ef1ee0051a427_1056900776692445796._call_sampler_star
File "stanfit4anon_model_39368d80adc693f1938ef1ee0051a427_1056900776692445796.pyx", line 406, in stanfit4anon_model_39368d80adc693f1938ef1ee0051a427_1056900776692445796._call_sampler
RuntimeError: Initialization failed.
"""
The above exception was the direct cause of the following exception:
RuntimeError Traceback (most recent call last)
<ipython-input-93-c99474c6b026> in <module>
----> 1 fit = sm.sampling(
2 data=dict(nStudy=nStudy,Y=Y),
3 warmup=500,
4 iter=1000,
5 chains=4,
~/.conda/envs/pystan-env/lib/python3.8/site-packages/pystan/model.py in sampling(self, data, pars, chains, iter, warmup, thin, seed, init, sample_file, diagnostic_file, verbose, algorithm, control, n_jobs, **kwargs)
811 call_sampler_args = izip(itertools.repeat(data), args_list, itertools.repeat(pars))
812 call_sampler_star = self.module._call_sampler_star
--> 813 ret_and_samples = _map_parallel(call_sampler_star, call_sampler_args, n_jobs)
814 samples = [smpl for _, smpl in ret_and_samples]
815
~/.conda/envs/pystan-env/lib/python3.8/site-packages/pystan/model.py in _map_parallel(function, args, n_jobs)
83 try:
84 pool = multiprocessing.Pool(processes=n_jobs)
---> 85 map_result = pool.map(function, args)
86 finally:
87 pool.close()
~/.conda/envs/pystan-env/lib/python3.8/multiprocessing/pool.py in map(self, func, iterable, chunksize)
362 in a list that is returned.
363 '''
--> 364 return self._map_async(func, iterable, mapstar, chunksize).get()
365
366 def starmap(self, func, iterable, chunksize=None):
~/.conda/envs/pystan-env/lib/python3.8/multiprocessing/pool.py in get(self, timeout)
769 return self._value
770 else:
--> 771 raise self._value
772
773 def _set(self, i, obj):
RuntimeError: Initialization failed.
```

STAN ERROR from TERMINAL (this is the end of the terminal output but it pretty much repeats this A LOT):

```
...
...
...
Rejecting initial value:
Initialization between (-2, 2) failed after 100 attempts.
Initialization between (-2, 2) failed after 100 attempts.
Try specifying initial values, reducing ranges of constrained values, or reparameterizing the model.
Rejecting initial value:
Error evaluating the log probability at the initial value.
Try specifying initial values, reducing ranges of constrained values, or reparameterizing the model.
Error evaluating the log probability at the initial value.
Exception: binomial_lpmf: Successes variable[4] is 19, but must be in the interval [0, 11] (in 'unknown file name' at line 20)
Exception: binomial_lpmf: Successes variable[4] is 19, but must be in the interval [0, 11] (in 'unknown file name' at line 20)
Initialization between (-2, 2) failed after 100 attempts.
Try specifying initial values, reducing ranges of constrained values, or reparameterizing the model.
Rejecting initial value:
Error evaluating the log probability at the initial value.
Exception: binomial_lpmf: Successes variable[4] is 19, but must be in the interval [0, 11] (in 'unknown file name' at line 20)
***
```