# API question: What are the semantics of array-style indexing on a Distribution object, with another PyMC object?

**URL:** <https://discourse.pymc.io/t/api-question-what-are-the-semantics-of-array-style-indexing-on-a-distribution-object-with-another-pymc-object/9343>\
**Category:** version agnostic\
**Tags:** doc\
**Created:** [May 6, 2022, 7:20am UTC](https://discourse.pymc.io/t/api-question-what-are-the-semantics-of-array-style-indexing-on-a-distribution-object-with-another-pymc-object/9343 "2022-05-06T07:20:08Z")\
**Posts on this page:** 3\
**Page:** 1

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**Author:** ![mdrum](https://avatars.discourse-cdn.com/v4/letter/m/a9adbd/32.png) [@mdrum](https://discourse.pymc.io/u/mdrum)\
**Post date:** [May 6, 2022, 7:20am UTC](https://discourse.pymc.io/t/api-question-what-are-the-semantics-of-array-style-indexing-on-a-distribution-object-with-another-pymc-object/9343/1 "2022-05-06T07:20:08Z")

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I am new to PyMC and I am studying the [Simpson’s Paradox](https://docs.pymc.io/en/v3/pymc-examples/examples/generalized_linear_models/GLM-simpsons-paradox.html) tutorial. The last line in Models 2 and 3 (cells 12 and 17) is

`pm.Normal("y", mu=μ, sigma=sigma[g], observed=data.y, dims="observation")`

where `sigma` is previously bound to a `pm.HalfCauchy`, i.e.,

`sigma = pm.HalfCauchy("sigma", beta=2, dims="group")`

ad `g` to an instance of `pm.Data`, i.e.,

`g = pm.Data("g", data.group_idx, dims="observation")`

I am wondering about the semantics of `sigma[g]`. Evidently, ` __getitem__ ` has been overridden on `pm.HalfCauchy` so that indexing into it with a `pm.Data` instance makes sense (note that the result of the indexing operation is an `AdvancedSubtensor.0`). But what does such an indexing operation mean in this context, and where might the override be documented? (Please note: I get the impression, from what I have seen in the docs and elsewhere so far, that this pattern of indexing into one PyMC object with another is rare; is my impression correct?).  
Thank you very much.

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**Author:** ![jessegrabowski](https://yyz2.discourse-cdn.com/flex036/user_avatar/discourse.pymc.io/jessegrabowski/32/5010_2.png) [@jessegrabowski](https://discourse.pymc.io/u/jessegrabowski)\
**Post date:** [May 6, 2022, 8:58am UTC](https://discourse.pymc.io/t/api-question-what-are-the-semantics-of-array-style-indexing-on-a-distribution-object-with-another-pymc-object/9343/2 "2022-05-06T08:58:35Z")

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Theano/Aesara tensors (and by extension PyMC variables) can be indexed exactly as numpy arrays. [The numpy documentation on integer-array indexing](https://numpy.org/doc/stable/user/basics.indexing.html#integer-array-indexing) should answer your question.

The long and short of it is that given some array, you can use the items in that array to create a new array of arbitrary length. In the case of the tutorial, `sigma` is a tensor of shape `(4,)`, and `g` is a `(100,)` array of `[0, 0, ..., 1, 1, ..., 2, 2, ... 3, 3, ...3]`. Indexing `sigma[g]` returns a `(100,)` tensor where the ith element corresponds to `sigma[g[i]]`.

> [@mdrum](#):
>
> (Please note: I get the impression, from what I have seen in the docs and elsewhere so far, that this pattern of indexing into one PyMC object with another is rare; is my impression correct?).

Au contraire, this is a very common way to write down a hierarchical model.

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**Author:** ![mdrum](https://avatars.discourse-cdn.com/v4/letter/m/a9adbd/32.png) [@mdrum](https://discourse.pymc.io/u/mdrum)\
**Post date:** [May 9, 2022, 3:16am UTC](https://discourse.pymc.io/t/api-question-what-are-the-semantics-of-array-style-indexing-on-a-distribution-object-with-another-pymc-object/9343/3 "2022-05-09T03:16:34Z")

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Thank you for your kind reply and pointers!