Assessment of calibration in binomial prediction models.

# Calibration Belt

## Installation

`pip install calibration-belt`

```import pandas as pd
from pathlib import Path
from calibration import CalibrationBelt

import matplotlib.pyplot as plt
%matplotlib inline
```

```df = pd.read_csv(Path('tests/data/example_data.csv'))

# Separate P (outcome) and E (probability outputed by the model)
# In this case we will evaluate two different models
P = df.target.to_numpy()
predictors = {
'SVM': df.SVM.to_numpy(),
'NN': df.NN.to_numpy()
}
```

## CalibrationBelt object

```# We create CalibrationBelt objects for
# each model we want to evaluate
belts = {}
for key, E in predictors.items():
belts[key] = CalibrationBelt(P, E)
```

## Plotting the belt

```# Calculate belt in the confidence intervals .8 and .95
for model, belt in belts.items():
fig, ax  = belt.plot(confidences=[.8, .95])
ax.set_title(model, fontsize=30)
```

## Calculating T-statistic and p_value

```for model, belt in belts.items():
T, p_value = belt.test()
print(f"Model: {model:3}, T-statistic: {T:08.5f} , p-value: {p_value:07.5f}")
```
``````Model: SVM, T-statistic: 08.37500 , p-value: 0.01518
Model: NN , T-statistic: 31.05418 , p-value: 0.00001
``````

## Calculating boundaries of the belt

```boundaries = belt.calculate_boundaries(.95)
lower, upper = boundaries[0, 1:]
print(f"Lower bound: {lower:.4f}, Upper bound: {upper:.4f}")
```
``````Lower bound: 0.0000, Upper bound: 0.0493
``````

## Cumulative distribution function

The plot below shows the computed distribution of the T-statistic in polynomials of degree m.

```T = [i / 10 for i in range(0, 301)]
viridis = plt.cm.get_cmap("viridis", 4)
fig, ax = plt.subplots(1, figsize=[10, 7])
for m in [1, 2, 3, 4]:
cdf = []
for t in T:
cdf.append(CalibrationBelt.calculate_cdf(t, m, .8))
ax.plot(T, cdf, color=viridis(m-1))
```

# References

Based on `Nattino, Giovanni, Stefano Finazzi, and Guido Bertolini. "A new calibration test and a reappraisal of the calibration belt for the assessment of prediction models based on dichotomous outcomes." Statistics in medicine 33.14 (2014): 2390-2407.`