# Error while sampling from Binomial with large n

**URL:** <https://discourse.pymc.io/t/error-while-sampling-from-binomial-with-large-n/11002>\
**Category:** v5\
**Tags:** modeling\
**Created:** [December 14, 2022, 4:18am UTC](https://discourse.pymc.io/t/error-while-sampling-from-binomial-with-large-n/11002 "2022-12-14T04:18:42Z")\
**Posts on this page:** 5\
**Page:** 1

<div class="post-metadata">

**Author:** ![Gireesh\_Ramji](https://yyz2.discourse-cdn.com/flex036/user_avatar/discourse.pymc.io/gireesh_ramji/32/4924_2.png) [@Gireesh\_Ramji](https://discourse.pymc.io/u/Gireesh_Ramji)\
**Post date:** [December 14, 2022, 4:18am UTC](https://discourse.pymc.io/t/error-while-sampling-from-binomial-with-large-n/11002/1 "2022-12-14T04:18:42Z")

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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:

```auto
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:

 ![Screen Shot 2022-12-14 at 3.07.40 PM](https://canada1.discourse-cdn.com/flex036/uploads/pymc3/original/2X/6/6fe1ea2f89fec65c4bba85240b00e5a8ee5a84e3.png)

Stack Trace of the error:

```auto
---------------------------------------------------------------------------
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}

```

---

<div class="post-metadata">

**Author:** ![ricardoV94](https://yyz2.discourse-cdn.com/flex036/user_avatar/discourse.pymc.io/ricardov94/32/5775_2.png) [@ricardoV94](https://discourse.pymc.io/u/ricardoV94)\
**Post date:** [December 14, 2022, 5:58am UTC](https://discourse.pymc.io/t/error-while-sampling-from-binomial-with-large-n/11002/2 "2022-12-14T05:58:42Z")

</div>

With a large enough number you will eventually fall out of the numerical support of the logp expression of any distribution and start seeing underflow/overflow issues.

---

<div class="post-metadata">

**Author:** ![Gireesh\_Ramji](https://yyz2.discourse-cdn.com/flex036/user_avatar/discourse.pymc.io/gireesh_ramji/32/4924_2.png) [@Gireesh\_Ramji](https://discourse.pymc.io/u/Gireesh_Ramji)\
**Post date:** [December 14, 2022, 6:31am UTC](https://discourse.pymc.io/t/error-while-sampling-from-binomial-with-large-n/11002/3 "2022-12-14T06:31:29Z")

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Thanks @ricardoV94 any suggestions on how I should handle the situation? This is coming from a use case where we are modeling binomial outcomes for a large number of programmatic ad impressions, so the numbers are really at this scale.

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<div class="post-metadata">

**Author:** ![ricardoV94](https://yyz2.discourse-cdn.com/flex036/user_avatar/discourse.pymc.io/ricardov94/32/5775_2.png) [@ricardoV94](https://discourse.pymc.io/u/ricardoV94)\
**Post date:** [December 14, 2022, 6:50am UTC](https://discourse.pymc.io/t/error-while-sampling-from-binomial-with-large-n/11002/4 "2022-12-14T06:50:44Z")

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At those scales you can either approximate the binomial with a normal (in which case you can rescale the data as well) or perhaps rescale your binomial data, without much loss of accuracy: [Binomial distribution - Wikipedia](https://en.wikipedia.org/wiki/Binomial_distribution#Normal_approximation)

---

<div class="post-metadata">

**Author:** ![Gireesh\_Ramji](https://yyz2.discourse-cdn.com/flex036/user_avatar/discourse.pymc.io/gireesh_ramji/32/4924_2.png) [@Gireesh\_Ramji](https://discourse.pymc.io/u/Gireesh_Ramji)\
**Post date:** [December 20, 2022, 5:37am UTC](https://discourse.pymc.io/t/error-while-sampling-from-binomial-with-large-n/11002/5 "2022-12-20T05:37:49Z")

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Thanks @ricardoV94 that seems to work