Introduction to Bayesian A/B Testing notebook produces SamplingError in version 5.16.2

Notebook title:Introduction to Bayesian A/B Testing
Notebook url:https://github.com/pymc-devs/pymc-examples/blob/main/examples/causal_inference/bayesian_ab_testing_introduction.ipynb

Issue description

Running the notebook produces:

A lot of:

pytensor\tensor\elemwise.py:763: RuntimeWarning: invalid value encountered in log
variables = ufunc(*ufunc_args, **ufunc_kwargs)

Then:

Cell In[14], line 1
----> 1 trace_weak, trace_strong = run_scenario_twovariant(
      2     variants=["A", "B"],
      3     true_rates=[0.23, 0.23],
      4     samples_per_variant=100000,
      5     weak_prior=BetaPrior(alpha=100, beta=100),
      6     strong_prior=BetaPrior(alpha=10000, beta=10000),
      7 )

Cell In[13], line 11, in run_scenario_twovariant(variants, true_rates, samples_per_variant, weak_prior, strong_prior)
      9 data = [BinomialData(**generated[v].to_dict()) for v in variants]
     10 with ConversionModelTwoVariant(priors=weak_prior).create_model(data):
---> 11     trace_weak = pm.sample(draws=5000)
     12 with ConversionModelTwoVariant(priors=strong_prior).create_model(data):
     13     trace_strong = pm.sample(draws=5000)

File ~\anaconda3\envs\pymc_env\Lib\site-packages\pymc\sampling\mcmc.py:776, in sample(draws, tune, chains, cores, random_seed, progressbar, progressbar_theme, step, var_names, nuts_sampler, initvals, init, jitter_max_retries, n_init, trace, discard_tuned_samples, compute_convergence_checks, keep_warning_stat, return_inferencedata, idata_kwargs, nuts_sampler_kwargs, callback, mp_ctx, blas_cores, model, **kwargs)
    774 ip: dict[str, np.ndarray]
    775 for ip in initial_points:
--> 776     model.check_start_vals(ip)
    777     _check_start_shape(model, ip)
    779 if var_names is not None:

File ~\anaconda3\envs\pymc_env\Lib\site-packages\pymc\model\core.py:1793, in Model.check_start_vals(self, start)
   1790 initial_eval = self.point_logps(point=elem)
   1792 if not all(np.isfinite(v) for v in initial_eval.values()):
-> 1793     raise SamplingError(
   1794         "Initial evaluation of model at starting point failed!\n"
   1795         f"Starting values:\n{elem}\n\n"
   1796         f"Logp initial evaluation results:\n{initial_eval}\n"
   1797         "You can call `model.debug()` for more details."
   1798     )

SamplingError: Initial evaluation of model at starting point failed!
Starting values:
{'p_logodds__': array([nan, nan])}

Logp initial evaluation results:
{'p': nan, 'y': -inf}
You can call `model.debug()` for more details.

ALSO:
strong/weak_prior name in function run_scenario_twovariant shadows a variabe with a different type in the outer scope. It's probably worth fixing this for readability.

Proposed solution

I don't know how to solve main problem

Suggest changing strong/weak_prior to strong/weak_prior_model in outer scope.

Start with examples/causal_inference/bayesian_ab_testing_introduction.ipynb and run the failing run_scenario_twovariant cell using PyMC 5.16.2. Investigate the reported invalid log values and SamplingError, and review the strong_prior/weak_prior shadowing noted in the issue. Done means the notebook runs without the reported failure and the variable naming is clear.