# How to account for multiple betas in example documentation?

**URL:** <https://discourse.pymc.io/t/how-to-account-for-multiple-betas-in-example-documentation/10992>\
**Category:** v5\
**Created:** [December 12, 2022, 7:43pm UTC](https://discourse.pymc.io/t/how-to-account-for-multiple-betas-in-example-documentation/10992 "2022-12-12T19:43:10Z")\
**Posts on this page:** 6\
**Page:** 1

<div class="post-metadata">

**Author:** ![localh](https://yyz2.discourse-cdn.com/flex036/user_avatar/discourse.pymc.io/localh/32/3721_2.png) [@localh](https://discourse.pymc.io/u/localh)\
**Post date:** [December 12, 2022, 7:43pm UTC](https://discourse.pymc.io/t/how-to-account-for-multiple-betas-in-example-documentation/10992/1 "2022-12-12T19:43:10Z")

</div>

How would I account for for multiple beta parameters in the toy example :[Prior and Posterior Predictive Checks — PyMC 4.4.0 documentation](https://www.pymc.io/projects/docs/en/stable/learn/core_notebooks/posterior_predictive.html#)

In this situation, where I do not just have `b`, but `b1`, `b2`, … etc.

```auto
post = idata.posterior
mu_pp = post["a"] + post["b"] * xr.DataArray(predictor_scaled, dims=["obs_id"]

```

---

<div class="post-metadata">

**Author:** ![cluhmann](https://yyz2.discourse-cdn.com/flex036/user_avatar/discourse.pymc.io/cluhmann/32/3083_2.png) [@cluhmann](https://discourse.pymc.io/u/cluhmann)\
**Post date:** [December 13, 2022, 4:49am UTC](https://discourse.pymc.io/t/how-to-account-for-multiple-betas-in-example-documentation/10992/2 "2022-12-13T04:49:55Z")

</div>

It depends on whether each coeffcient was a separate parameter or if you have a parameter array (e.g., `betas=pm.Normal("betas, dims="obs_id")`). If they are separate, you could just do something along these lines:

```python
mu_pp = (
        post["a"] + 
        post["b1"] * xr.DataArray(predictor_1, dims=["obs_id"] +
        post["b2"] * xr.DataArray(predictor_2, dims=["obs_id"] +
        post["b3"] * xr.DataArray(predictor_3, dims=["obs_id"]
        )

```

Following that example, however, it would be easier to just save the predicted means like this:

```python
with pm.Model() as model_1:
    a = pm.Normal("a", 0.0, 0.5)
    b = pm.Normal("b", 0.0, 1.0)

    mu = pm.Deterministic("mu", a + b * predictor_scaled)
    sigma = pm.Exponential("sigma", 1.0)

    pm.Normal("obs", mu=mu, sigma=sigma, observed=outcome_scaled)
    idata = pm.sample_prior_predictive(samples=50, random_seed=rng)

```

And then you should be able to do something like this:

```python
plt.scatter(predictor_scaled, post["mu"].mean(("chain", "draw")))

```

Not 100% on any of that code running as-is, but should get you started. If not, feel free to ask.

---

<div class="post-metadata">

**Author:** ![localh](https://yyz2.discourse-cdn.com/flex036/user_avatar/discourse.pymc.io/localh/32/3721_2.png) [@localh](https://discourse.pymc.io/u/localh)\
**Post date:** [December 13, 2022, 11:30am UTC](https://discourse.pymc.io/t/how-to-account-for-multiple-betas-in-example-documentation/10992/3 "2022-12-13T11:30:41Z")

</div>

Thanks, super helpful! Could you recommend a procedure if the betas were all chained together, say:

```auto
with pm.Model() as model_1:
    a = pm.Normal("a", 0.0, 10.0)
    betas = pm.Normal('betas', mu=[40, 25, 55], sigma=5, dims='features')
    ...

```

Or should we stick to making discrete entries for each parameter (to make our lives easier later?)

Also in your example, where does `idata` come into play; it seems as an unused variable.

---

<div class="post-metadata">

**Author:** ![cluhmann](https://yyz2.discourse-cdn.com/flex036/user_avatar/discourse.pymc.io/cluhmann/32/3083_2.png) [@cluhmann](https://discourse.pymc.io/u/cluhmann)\
**Post date:** [December 15, 2022, 7:48pm UTC](https://discourse.pymc.io/t/how-to-account-for-multiple-betas-in-example-documentation/10992/4 "2022-12-15T19:48:28Z")

</div>

`idata` was in there just because it was leftover from the example notebook. Here is a little example that uses a parameter array of coefficients. It could be simplified further, but maybe it helps.

```python
import pymc as pm
import numpy as np
import xarray as xr
import arviz as az
import matplotlib.pyplot as plt

nObs = 100
nPredictors = 3

xs = np.random.random(size = (nPredictors,nObs))
obs = 1 + np.dot(xs.T, [1,2,3])

with pm.Model() as model:
    a = pm.Normal("a", 0.0, 10.0)
    betas = pm.Normal('betas', mu=0, sigma=5, shape=nPredictors)
    mu = pm.Deterministic("mu", a + pm.math.dot(betas, xs))
    pm.Normal("obs", mu=mu, sigma=1, observed=obs)
    idata = pm.sample()

post = idata.posterior
a = az.extract(idata.posterior, var_names="a", combined=True)
b = az.extract(idata.posterior, var_names="betas", combined=True)
mu_pp = np.tile(a,(nObs,1)) + np.dot(xs.T, b)

plt.scatter(obs, np.mean(mu_pp, axis=1))
plt.show()

```

---

<div class="post-metadata">

**Author:** ![localh](https://yyz2.discourse-cdn.com/flex036/user_avatar/discourse.pymc.io/localh/32/3721_2.png) [@localh](https://discourse.pymc.io/u/localh)\
**Post date:** [December 15, 2022, 8:19pm UTC](https://discourse.pymc.io/t/how-to-account-for-multiple-betas-in-example-documentation/10992/5 "2022-12-15T20:19:51Z")

</div>

Very cool – excited to play with this!

---

<div class="post-metadata">

**Author:** ![OriolAbril](https://yyz2.discourse-cdn.com/flex036/user_avatar/discourse.pymc.io/oriolabril/32/2497_2.png) [@OriolAbril](https://discourse.pymc.io/u/OriolAbril)\
**Post date:** [December 16, 2022, 12:36am UTC](https://discourse.pymc.io/t/how-to-account-for-multiple-betas-in-example-documentation/10992/6 "2022-12-16T00:36:19Z")

</div>

I want to add the xarray version of this too if you don’t mind, which gets the same result as the numpy code above:

Provided you label your dimensions in the model:

```auto
with pm.Model() as model:
    x = pm.ConstantData("x", xs, dims=("predictor", "obs_id"))
    a = pm.Normal("a", 0.0, 10.0)
    betas = pm.Normal('betas', mu=0, sigma=5, dims="predictor")
    mu = pm.Deterministic("mu", a + pm.math.dot(betas, xs), dims="obs_id")
    pm.Normal("obs", mu=mu, sigma=1, observed=obs, dims="obs_id")
    idata = pm.sample()

```

You can then do:

```auto
a = az.extract(idata, var_names="a")
b = az.extract(idata, var_names="betas")

mu_pp = a + xr.dot(idata.constant_data["x"], b, dims="predictor")

plt.scatter(obs, mu_pp.mean("sample"))
plt.show()

```

Note the definition of `a` and `b` would also work if used in the code above, `extract` defaults to returning combined variables from the posterior (unless a different group is specified).

Later, instead of indicating what dimension to reduce with the tiling, transposing or using integer axis ids, we do so by name. We reduce the predictor dimension in the dot product, and the sample dimension in the mean, so we are only left with the obs\_id dim which is the one we want to plot.