# Adding a Deterministic variable after sampling

**URL:** <https://discourse.pymc.io/t/adding-a-deterministic-variable-after-sampling/13236>\
**Category:** v5\
**Created:** [November 3, 2023, 6:32am UTC](https://discourse.pymc.io/t/adding-a-deterministic-variable-after-sampling/13236 "2023-11-03T06:32:53Z")\
**Posts on this page:** 7\
**Page:** 1

<div class="post-metadata">

**Author:** ![mike-lawrence](https://yyz2.discourse-cdn.com/flex036/user_avatar/discourse.pymc.io/mike-lawrence/32/4913_2.png) [@mike-lawrence](https://discourse.pymc.io/u/mike-lawrence)\
**Post date:** [November 3, 2023, 6:32am UTC](https://discourse.pymc.io/t/adding-a-deterministic-variable-after-sampling/13236/1 "2023-11-03T06:32:53Z")

</div>

I have a model where there are a number of variables derived from the parameters that are of interest, but declaring them all Deterministic so they appear in the InferenceData output causes slower sampling than if declare them as Deterministic. I know I can do things by hand with the Xarray representations of the posterior variables, but I’m curious if there’s a more straightforward way involving adding them as new Deterministic-declared variables to the model object after sampling and calling something akin to `pm.sample_posterior_predictive(trace)` (but without any stochasticity). Or is there genuinely no option but to compute them by hand with the Xarrays?

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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:** [November 3, 2023, 9:44am UTC](https://discourse.pymc.io/t/adding-a-deterministic-variable-after-sampling/13236/2 "2023-11-03T09:44:19Z")

</div>

You can indeed use `sample_posterior_predictive` without any stochasticity (unless the deterministic depends on an observed variable, does it?).

---

<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:** [November 3, 2023, 10:53am UTC](https://discourse.pymc.io/t/adding-a-deterministic-variable-after-sampling/13236/3 "2023-11-03T10:53:06Z")

</div>

Here is a snippet:

```python
import pymc as pm
import numpy as np

from pymc.model.fgraph import clone_model

with pm.Model() as m:
    x = pm.Beta("x", 1, 1)
    idata = pm.sample(progressbar=False)
    
with clone_model(m) as clone_m:
    det = pm.Deterministic("det", clone_m["x"] + 1)
    pp = pm.sample_posterior_predictive(idata, var_names=["det"], progressbar=False)
    
assert np.all(pp.posterior_predictive["det"] == idata.posterior["x"] + 1)

```

```python
Auto-assigning NUTS sampler...
Initializing NUTS using jitter+adapt_diag...
Multiprocess sampling (4 chains in 4 jobs)
NUTS: [x]
Sampling 4 chains for 1_000 tune and 1_000 draw iterations (4_000 + 4_000 draws total) took 2 seconds.
Sampling: []

```

Node the second `Sampling: []` corresponding to `sample_posterior_predictive`, meaning there is nothing stochastic in it.

I used `clone_model` to not modify the original model, but if you are not concerned about it you can add the Deterministic on the original model after sampling.

If you need a Deterministic that depends on the values of the observed variable, you can replace the observed variable by it’s data with `pm.do` instead of just doing `clone_model`.

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<div class="post-metadata">

**Author:** ![mike-lawrence](https://yyz2.discourse-cdn.com/flex036/user_avatar/discourse.pymc.io/mike-lawrence/32/4913_2.png) [@mike-lawrence](https://discourse.pymc.io/u/mike-lawrence)\
**Post date:** [November 4, 2023, 12:22am UTC](https://discourse.pymc.io/t/adding-a-deterministic-variable-after-sampling/13236/4 "2023-11-04T00:22:20Z")

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> [@ricardoV94](#):
>
> det = pm.Deterministic(“det”, clone\_m[“x”] + 1)

Do the new deterministic variables have to be functions of parameter variables or other existing deterministic variables as in this case? In my case, I have a whole chain of derived variables and it’s only the last that I’d like the values for after sampling, akin to:

```python
with pm.Model() as model:
    # priors
    ...
    # derived variables
    ...
    interesting_dv = ... # interesting dv computed from earlier uninteresting vars
    # likelihood
    ...

```

---

<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:** [November 4, 2023, 9:09am UTC](https://discourse.pymc.io/t/adding-a-deterministic-variable-after-sampling/13236/5 "2023-11-04T09:09:44Z")

</div>

> [@mike-lawrence](#):
>
> Do the new deterministic variables have to be functions of parameter variables or other existing deterministic

Yes, because the values from the trace will be used as inputs in the posterior predictive function.

You can always have a helper function that returns the uninteresting variables from the model variables to avoid code duplication if that’s the concern?

---

<div class="post-metadata">

**Author:** ![mike-lawrence](https://yyz2.discourse-cdn.com/flex036/user_avatar/discourse.pymc.io/mike-lawrence/32/4913_2.png) [@mike-lawrence](https://discourse.pymc.io/u/mike-lawrence)\
**Post date:** [November 4, 2023, 11:48pm UTC](https://discourse.pymc.io/t/adding-a-deterministic-variable-after-sampling/13236/6 "2023-11-04T23:48:24Z")

</div>

Hm, I’m getting different values for even Deterministic quantities when I declare them in this way. Here’s a minimal example:

```python
import pymc as pm
from pymc.model.fgraph import clone_model

with pm.Model() as model:
    data = pm.ConstantData('data',[0])
    mu = pm.Normal('mu', mu=0, sigma=1)
    mu_squared1 = pm.Deterministic('mu_squared1', mu**2)
    y = pm.Normal('y', mu=mu, sigma=1, observed=data)

with clone_model(model) as model2:
    mu_squared2 = pm.Deterministic('mu_squared2', mu**2)

with model2:
    trace = pm.sample_prior_predictive(
        samples = 1
        , var_names = ['mu','mu_squared1','mu_squared2']
    )

```

Which yields:

```auto
>>> trace['prior']['mu']
array([[-1.44118118]])

>>> trace['prior']['mu_squared1']
array([[2.0770032]])

>>> trace['prior']['mu_squared2']
array([[0.25616674]])

```

---

<div class="post-metadata">

**Author:** ![mike-lawrence](https://yyz2.discourse-cdn.com/flex036/user_avatar/discourse.pymc.io/mike-lawrence/32/4913_2.png) [@mike-lawrence](https://discourse.pymc.io/u/mike-lawrence)\
**Post date:** [November 4, 2023, 11:57pm UTC](https://discourse.pymc.io/t/adding-a-deterministic-variable-after-sampling/13236/7 "2023-11-04T23:57:37Z")

</div>

Oh, I failed to notice that one can’t simply refer to variables as normal when cloning but have to refer to them as elements of the cloned model object, so this works as expected:

```python
import pymc as pm
from pymc.model.fgraph import clone_model

with pm.Model() as model:
    data = pm.ConstantData('data',[0])
    mu = pm.Normal('mu', mu=0, sigma=1)
    mu_squared1 = pm.Deterministic('mu_squared1', mu**2)
    y = pm.Normal('y', mu=mu, sigma=1, observed=data)

with clone_model(model) as model2:
    mu_squared2 = pm.Deterministic('mu_squared2', model2['mu']**2)

with model2:
    trace = pm.sample_prior_predictive(
        samples = 1
        , var_names = ['mu','mu_squared1','mu_squared2']
    )

```