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This is a minimal reproducible example of Poisson regression to predict counts using dummy data.
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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.
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For more statistical detail see:
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+ Basic info on [Wikipedia](https://en.wikipedia.org/wiki/Poisson_regression)
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+ GLMs: Poisson regression, exposure, and overdispersion in Chapter 6.2 of [ARM, Gelmann & Hill 2006](http://www.stat.columbia.edu/%7Egelman/arm/)
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+ This worked example from ARM 6.2 by [Clay Ford](http://www.clayford.net/statistics/poisson-regression-ch-6-of-gelman-and-hill/)
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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.
This is a minimal reproducible example of Poisson regression to predict counts using dummy data.
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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.
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For more statistical detail see:
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+ Basic info on [Wikipedia](https://en.wikipedia.org/wiki/Poisson_regression)
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+ GLMs: Poisson regression, exposure, and overdispersion in Chapter 6.2 of [ARM, Gelmann & Hill 2006](http://www.stat.columbia.edu/%7Egelman/arm/)
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+ This worked example from ARM 6.2 by [Clay Ford](http://www.clayford.net/statistics/poisson-regression-ch-6-of-gelman-and-hill/)
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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.
This dummy dataset is created to emulate some data created as part of a study into quantified self, and the real data is more complicated than this. Ask Ian Osvald if you'd like to know more https://twitter.com/ianozsvald
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This dummy dataset is created to emulate some data created as part of a study into quantified self, and the real data is more complicated than this. Ask Ian Osvald if you'd like to know more [@ianozvald](https://twitter.com/ianozsvald).
We can use `az.plot_ppc()` to check that the posterior predictive samples are similar to the observed data.
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For more information on posterior predictive checks, we can refer to https://docs.pymc.io/notebooks/posterior_predictive.html.
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For more information on posterior predictive checks, we can refer to {ref}`pymc:posterior_predictive`.
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