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notebook: GLM Poisson regression, update header and footer #462

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nb: GLM poisson regression, update header/footer
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309 changes: 167 additions & 142 deletions examples/generalized_linear_models/GLM-poisson-regression.ipynb
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51 changes: 33 additions & 18 deletions myst_nbs/generalized_linear_models/GLM-poisson-regression.myst.md
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Original file line number Diff line number Diff line change
Expand Up @@ -6,15 +6,40 @@ jupytext:
format_version: 0.13
jupytext_version: 1.13.7
kernelspec:
display_name: pymc_env
display_name: pymc-ex
language: python
name: pymc_env
name: pymc-ex
---

+++ {"papermill": {"duration": 0.043172, "end_time": "2021-02-23T11:26:55.064791", "exception": false, "start_time": "2021-02-23T11:26:55.021619", "status": "completed"}, "tags": []}

(GLM-poisson-regression)=
# GLM: Poisson Regression

:::{post} November 12, 2022
:tags: regression, poisson
:category: Intermediate
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The flying dove in the preview: https://pymcio--462.org.readthedocs.build/projects/examples/en/462/generalized_linear_models/GLM-poisson-regression.html is not green because tagss and categories are case sensitive. it should be everything lowercase.

:author: Jonathan Sedar, Benjamin Vincent
:::

+++ {"papermill": {"duration": 0.069202, "end_time": "2021-02-23T11:27:01.489628", "exception": false, "start_time": "2021-02-23T11:27:01.420426", "status": "completed"}, "tags": []}

This is a minimal reproducible example of Poisson regression to predict counts using dummy data.

This Notebook is basically an excuse to demo Poisson regression using PyMC, both manually and using `bambi` to demo interactions using the `formulae` library. We will create some dummy data, Poisson distributed according to a linear model, and try to recover the coefficients of that linear model through inference.

For more statistical detail see:

+ Basic info on [Wikipedia](https://en.wikipedia.org/wiki/Poisson_regression)
+ GLMs: Poisson regression, exposure, and overdispersion in Chapter 6.2 of [ARM, Gelmann & Hill 2006](http://www.stat.columbia.edu/%7Egelman/arm/)
+ This worked example from ARM 6.2 by [Clay Ford](http://www.clayford.net/statistics/poisson-regression-ch-6-of-gelman-and-hill/)

This very basic model is inspired by [a project by Ian Osvald](http://ianozsvald.com/2016/05/07/statistically-solving-sneezes-and-sniffles-a-work-in-progress-report-at-pydatalondon-2016/), which is concerned with understanding the various effects of external environmental factors upon the allergic sneezing of a test subject.

```{code-cell} ipython3
#!pip install seaborn
```

```{code-cell} ipython3
---
papermill:
Expand Down Expand Up @@ -53,20 +78,6 @@ rng = np.random.default_rng(RANDOM_SEED)
az.style.use("arviz-darkgrid")
```

+++ {"papermill": {"duration": 0.069202, "end_time": "2021-02-23T11:27:01.489628", "exception": false, "start_time": "2021-02-23T11:27:01.420426", "status": "completed"}, "tags": []}

This is a minimal reproducible example of Poisson regression to predict counts using dummy data.

This Notebook is basically an excuse to demo Poisson regression using PyMC3, both manually and using `bambi` to demo interactions using the `formulae` library. We will create some dummy data, Poisson distributed according to a linear model, and try to recover the coefficients of that linear model through inference.

For more statistical detail see:

+ Basic info on [Wikipedia](https://en.wikipedia.org/wiki/Poisson_regression)
+ GLMs: Poisson regression, exposure, and overdispersion in Chapter 6.2 of [ARM, Gelmann & Hill 2006](http://www.stat.columbia.edu/%7Egelman/arm/)
+ This worked example from ARM 6.2 by [Clay Ford](http://www.clayford.net/statistics/poisson-regression-ch-6-of-gelman-and-hill/)

This very basic model is inspired by [a project by Ian Osvald](http://ianozsvald.com/2016/05/07/statistically-solving-sneezes-and-sniffles-a-work-in-progress-report-at-pydatalondon-2016/), which is concerned with understanding the various effects of external environmental factors upon the allergic sneezing of a test subject.

+++ {"papermill": {"duration": 0.06268, "end_time": "2021-02-23T11:27:01.615645", "exception": false, "start_time": "2021-02-23T11:27:01.552965", "status": "completed"}, "tags": []}

## Local Functions
Expand Down Expand Up @@ -489,7 +500,7 @@ posterior_predictive = model.predict(inf_fish_alt, kind="pps")

We can use `az.plot_ppc()` to check that the posterior predictive samples are similar to the observed data.

For more information on posterior predictive checks, we can refer to https://docs.pymc.io/notebooks/posterior_predictive.html.
For more information on posterior predictive checks, we can refer to {class}`pymc.posterior_predictive`.
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Suggested change
For more information on posterior predictive checks, we can refer to {class}`pymc.posterior_predictive`.
For more information on posterior predictive checks, we can refer to {ref}`pymc:posterior_predictive`.


```{code-cell} ipython3
az.plot_ppc(inf_fish_alt);
Expand All @@ -498,8 +509,9 @@ az.plot_ppc(inf_fish_alt);
+++ {"papermill": {"duration": 0.106366, "end_time": "2021-02-23T11:31:34.956844", "exception": false, "start_time": "2021-02-23T11:31:34.850478", "status": "completed"}, "tags": []}

## Authors
- Example originally contributed by Jonathan Sedar 2016-05-15 [github.com/jonsedar](https://github.com/jonsedar)
- Example originally contributed by [Jonathan Sedar](https://github.com/jonsedar) 2016-05-15.
- Updated to PyMC v4 by [Benjamin Vincent](https://github.com/drbenvincent) May 2022.
- Notebook header and footer updated November 2022.

+++

Expand All @@ -518,3 +530,6 @@ tags: []
%load_ext watermark
%watermark -n -u -v -iv -w -p aesara,aeppl
```

:::{include} ../page_footer.md
:::