I am facing the following issue with v4.2.2 (also tried with v5.0, but same issue persists):

Sampling from a Binomial with a beta prior seems to proceed without issues as long as the number of trials is <2.2bn, but for n >= 2.2bn the initial evaluation checks fail.

It also fails for 2.3bn and 3.0bn, but works well for smaller numbers.

Sharing code, screenshots and the stack trace of a minimal example to reproduce:

Code:

```
for n in [2100000000,2200000000]:
n = int(n)
exclusive_count = np.random.binomial(n=n,
p=0.25,
size=1)
print(f'Sampling with n = {n}, exclusive_count = {exclusive_count}')
with pm.Model() as model:
p_exclusive_id = pm.Beta('p_exclusive_id',
alpha=1.0,
beta=1.0)
n_exclusive_id = pm.Binomial('n_exclusive_id',
n = n,
p = p_exclusive_id,
observed = exclusive_count)
idata = pm.sample()
```

Execution Screenshot:

Stack Trace of the error:

```
---------------------------------------------------------------------------
SamplingError Traceback (most recent call last)
<ipython-input-33-b527c150c47a> in <module>
13 p = p_exclusive_id,
14 observed = exclusive_count)
---> 15 idata = pm.sample()
~/PycharmProjects/cross-system-reporting/venv/lib/python3.8/site-packages/pymc/sampling.py in sample(draws, step, init, n_init, initvals, trace, chains, cores, tune, progressbar, model, random_seed, discard_tuned_samples, compute_convergence_checks, callback, jitter_max_retries, return_inferencedata, idata_kwargs, mp_ctx, **kwargs)
559 # One final check that shapes and logps at the starting points are okay.
560 for ip in initial_points:
--> 561 model.check_start_vals(ip)
562 _check_start_shape(model, ip)
563
~/PycharmProjects/cross-system-reporting/venv/lib/python3.8/site-packages/pymc/model.py in check_start_vals(self, start)
1799
1800 if not all(np.isfinite(v) for v in initial_eval.values()):
-> 1801 raise SamplingError(
1802 "Initial evaluation of model at starting point failed!\n"
1803 f"Starting values:\n{elem}\n\n"
SamplingError: Initial evaluation of model at starting point failed!
Starting values:
{'p_exclusive_id_logodds__': array(0.22135405)}
Initial evaluation results:
{'p_exclusive_id': -1.4, 'n_exclusive_id': -inf}
```