# Sampling errors when running hierarchical model using hyperpriors

**URL:** <https://discourse.pymc.io/t/sampling-errors-when-running-hierarchical-model-using-hyperpriors/8226>\
**Category:** Questions\
**Created:** [October 26, 2021, 8:12pm UTC](https://discourse.pymc.io/t/sampling-errors-when-running-hierarchical-model-using-hyperpriors/8226 "2021-10-26T20:12:51Z")\
**Posts on this page:** 1\
**Page:** 1

<div class="post-metadata">

**Author:** ![michnag](https://yyz2.discourse-cdn.com/flex036/user_avatar/discourse.pymc.io/michnag/32/3376_2.png) [@michnag](https://discourse.pymc.io/u/michnag)\
**Post date:** [October 26, 2021, 8:12pm UTC](https://discourse.pymc.io/t/sampling-errors-when-running-hierarchical-model-using-hyperpriors/8226/1 "2021-10-26T20:12:51Z")

</div>

I have the following hierarchical model, where `y` is `101x13`, `X_1` is `101x13x26` and `X_2` is `101x41`.  
There are 101 groups, 13 observations per group, 26 level 1 features (`K_1`) and 41 level 2 features (`K_2`).

```auto
with pm.Model() as model:
    # Hyperpriors
    mu_v_2 = pm.Normal(name="mu_v_2", mu=0.0, sigma=1.0, shape=())
    mu_K_2 = pm.Normal(name="mu_K_2", mu=0.0, sigma=1.0, shape=(n_vars_2, 1))
    mu_K_1 = pm.Normal(name="mu_K_1", mu=0.0, sigma=1.0, shape=n_vars_1)
    sigma_v_2 = pm.HalfNormal(name="sigma_v_2", sigma=1.0, shape=())
    sigma_K_2 = pm.HalfNormal(name="sigma_K_2", sigma=1.0, shape=(n_vars_2, 1))
    sigma_K_1 = pm.HalfNormal(name="sigma_K_1", sigma=1, shape=n_vars_1)

    # Level 2 intercept
    v_2 = pm.Normal(name="v_2", mu=mu_v_2, sigma=sigma_v_2, shape=())

    # Level 2 variables
    K_2 = pm.Normal(name="K_2", mu=mu_K_2, sigma=sigma_K_2, shape=(n_vars_2, 1))

    # Level 1 intercept
    v_1 = pm.Deterministic(name="v_1", var=pm.math.dot(X_2, K_2) + v_2)

    # Level 1 variables
    K_1 = pm.Normal(name="K_1", mu=mu_K_1, sigma=sigma_K_1, shape=n_vars_1)

    # Model error
    eps_1 = pm.Gamma(name="eps_1", alpha=9.0, beta=4.0, shape=())

    # Model mean
    y_hat = pm.Deterministic(name="y_hat", var=pm.math.dot(X_1, K_1) + v_1)

    # Likelihood
    y_like = pm.Normal(name="y_like", mu=y_hat, sigma=eps_1, observed=y)

with model:
    trace = pm.sample(draws=5000, chains=2, tune=5000, init="auto", return_inferencedata=True,
                      random_seed=SEED, cores=1)

```

However, when I run the model, I get the following errors:

> There were 2982 divergences after tuning. Increase `target_accept` or reparameterize.  
> The acceptance probability does not match the target. It is 0.6530916769639405, but should be close to 0.8. Try to increase the number of tuning steps.  
> There were 6779 divergences after tuning. Increase `target_accept` or reparameterize.  
> The acceptance probability does not match the target. It is 0.40813842195230965, but should be close to 0.8. Try to increase the number of tuning steps.  
> The rhat statistic is larger than 1.2 for some parameters.  
> The estimated number of effective samples is smaller than 200 for some parameters.

If I run the model without using hyperpriors, the model works fine and there are no errors. I already tried different parameters for the hyperpriors and also increased draws and tune to 10,000 without success.

Moreover, it appears (when running without hyperpriors) that all level 2 features’ parameter are insignificant, which is quite unreasonable regarding the data at hand.