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# Model fitting

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Here, we will look at an example of fitting a model to an example dataset.

```{code-cell} ipython3
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---
%matplotlib inline
```

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First, we will import the necessary packages:

```{code-cell} ipython3
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import pymc as pm

import pylater
import pylater.data
```

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We will use the 50% condition from participant 'a' in the example data provided in `pylater`:

```{code-cell} ipython3
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dataset = pylater.data.cw1995["b_p50"]
```

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We can then build the model, using the default priors, via:

```{code-cell} ipython3
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model = pylater.build_default_model(datasets=[dataset])
```

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We can then fit the model by using the `sample` function from PyMC:

```{code-cell} ipython3
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with model:
    idata = pm.sample(chains=4)
```

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We can then use the posterior summary methods from PyMC to evaluate the posteriors:

```{code-cell} ipython3
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pm.stats.summary(data=idata)
```

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We can futher evaluate the model fit by examining the distribution of draws from the fitted model - the posterior predictive distribution (better described as the posterior *retrodictive* distribution; see ["Towards a principled Bayesian workflow" by Michael Betancourt](https://betanalpha.github.io/assets/case_studies/principled_bayesian_workflow.html#143_Posterior_Retrodiction_Checks)):

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First, we need to use PyMC to sample the posterior predictives:

```{code-cell} ipython3
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with model:
    idata = pm.sample_posterior_predictive(trace=idata, extend_inferencedata=True)
```

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We can then use the `plot_predictive` method of a `ReciprobitPlot` instance to visualise the posterior predictives:

```{code-cell} ipython3
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plot = pylater.ReciprobitPlot()
plot.plot_predictive(idata=idata, predictive_type="posterior");
```

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In the above, we can see the 95% credible interval and median of the distribution of posterior predictive samples.

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This becomes particularly useful when compared against the ECDF of the observed data:

```{code-cell} ipython3
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plot = pylater.ReciprobitPlot()
plot.plot_predictive(idata=idata, predictive_type="posterior");
plot.plot_data(data=dataset);
```

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We can see a reasonably good correspondence between the observations and the draws from the fitted model.

```{code-cell} ipython3
---
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%load_ext watermark
%watermark -n -u -v -iv -p matplotlib
```