Pymc Version: 5.7.2

PyTensor Version: 2.14.2

I have a model defined as follows. Note there is a loop to define several variables. I dont know if this is causing the loop fusion warning or not? I am not looping a pytensor object, just defining the variables in a simple for loop. Removing the for loop didnt remove the warnings nor did it impact the issue described below.

```
with pm.Model(coords=coords) as base_model:
# --- data containers ---
fs_ = pm.MutableData(name="fs", value=fm.values, dims= ("date", "fourier_mode"))
adstock_sat_media_ = pm.MutableData(name="asm", value = media_scaled, dims= ("date", "channel"))
target_ = pm.MutableData(name="target", value=target_scaled, dims = "date")
t_ = pm.MutableData(name="t", value=t_scaled, dims = "date")
response_mean = []
# --- intercept ---
intercept = pm.HalfNormal(name="intercept", sigma=2)
response_mean.append(intercept)
# --- trend ---
b_trend = pm.Normal(name="b_trend", mu=0, sigma=1)
k_trend = pm.Uniform('k_trend', 0.5, 1.5 )
trend = pm.Deterministic(name="trend", var = trend_func(t_,b_trend,k_trend))
response_mean.append(trend)
# --- seasonality ff ---
b_fourier = pm.Laplace(name="b_fourier", mu=0, b=1, dims= "fourier_mode")
seasonality_effect = pm.Deterministic(name="seasonality", var = pm.math.dot(fs_, b_fourier))
response_mean.append(seasonality_effect)
baseline_effect = pm.Deterministic(name="baseline", var = intercept+trend+seasonality_effect)
# --- adstock_saturation variables ---
for i in range(4):
var = media_variables[i]
# data
x = adstock_sat_media_[:,i]
# alpha,theta prior (adstock)
alpha = pm.Beta(name=f'alpha_{var}', alpha=1, beta=3)
theta = pm.Beta(name=f'theta_{var}', alpha=1, beta=1)
# beta prior
beta = pm.HalfNormal(name= f'b_{var}',sigma=2)
# saturation prior
mu_log_sat = pm.Gamma(name=f'mu_log_sat_{var}', alpha= 3, beta=1)
# effect
var_effect = pm.Deterministic(name=f'effect_{var}', var = beta * logistic_saturation(pt_adstock(x, alpha, l_max, True , True, theta ), mu_log_sat))
response_mean.append(var_effect)
# --- standard deviation of the normal likelihood ---
sigma = pm.HalfNormal(name="sigma", sigma=2)
# --- degrees of freedom of the t distribution ---
nu = pm.Gamma(name="nu", alpha=10, beta=2)
mu = pm.Deterministic(name="mu", var= sum(response_mean))
# --- likelihood ---
pm.StudentT(name="likelihood", nu=nu, mu=mu, sigma=sigma, observed=target_)
```

I’m using the numpyro sampler. This completes relatively quickly.

```
with base_model:
# --- trace --
base_model_trace =pm.sample(
nuts_sampler = "numpyro",
draws = 2000,
chains = 4,
idata_kwargs={"log_likelihood": True}
)
# --- posterior predictive distribution ---
base_model_posterior_predictive = pm.sample_posterior_predictive(
trace=base_model_trace, random_seed=rng
)
```

I am trying to make out of sample predictions by changing one of the inputs. This can take almost 2 minutes! If I re-run the initial sampling above, and then the sample_posterior_predictive cell below, it completed in ~3 seconds. Once this happens (it runs fast), it runs fast each time its re-ran.

```
%%time
media_new = mmm_dat[media_variables]
media_new['ctv_imp'] = media_new['ctv_imp']*1.1
media_new_scaled = exog_scalar.transform(media_new)
pm.set_data({"asm": media_new_scaled}, model = base_model)
pred_oos = pm.sample_posterior_predictive(trace = base_model_trace, model = base_model, predictions=True, extend_inferencedata=False, random_seed=rng)
```

But if I make a change to the cell , such as the proportion I multiply one of the inputs by

`media_new['ctv_imp'] = media_new['ctv_imp']*1.2`

the cell for sample_posterior_predictive takes several minutes.