# Build Conformal Prediction Intervals

Conformal prediction is a framework for constructing prediction intervals with a finite-sample coverage guarantee. Unlike parametric intervals, which require assumptions about the error distribution, conformal intervals are valid under any exchangeable data-generating process. The split conformal method reserves a calibration set during fitting, uses it to measure residual quantiles, and inflates the interval accordingly (a procedure that is simple, fast, and theoretically grounded).


# Fit

Load the `mcycle` dataset and fit a conformal predictor with the split method at a nominal 95% coverage level. The `seed` argument ensures reproducibility of the train/calibration split.


``` python
import numpy as np
import whittaker as wk

# Fit a split conformal predictor at 95% coverage
data = wk.load_dataset("mcycle")
predictor = wk.conformal_fit(
    "accel ~ s(times, k=15)",
    data=data,
    method="split",
    level=0.95,
    seed=23,
)
```


# Predict

Generate predictions on an evenly spaced grid across the observed time range. The result is a [ConformalResult](../reference/ConformalResult.md#whittaker.ConformalResult) with point predictions and interval bounds.


``` python
# Predict on a fine grid and inspect point estimates
new_data = {"times": np.linspace(data["times"].min(), data["times"].max(), 200)}
result = predictor.predict(new_data)
result.values[:5]
```


    array([3.70250183, 4.29428186, 4.88249012, 5.46090784, 6.0212509 ])


Inspect the lower and upper interval bounds separately.


``` python
result.lower[:5]
```


    array([-40.20727696, -39.61549693, -39.02728866, -38.44887094,
           -37.88852789])


``` python
result.upper[:5]
```


    array([47.61228061, 48.20406064, 48.7922689 , 49.37068663, 49.93102968])


# Verify Coverage

Compute empirical coverage on the training data. This measures the fraction of observed responses that fall within their respective prediction intervals.


``` python
wk.conformal_coverage(predictor, data, response="accel")
```


    0.9398496240601504


# Interpret

The empirical coverage should meet or exceed the nominal 0.95 level. This is not a coincidence or a tuning outcome but rather it is a finite-sample guarantee that holds as long as the training and test data are exchangeable. Unlike Bayesian credible intervals, which express posterior uncertainty under a model, conformal intervals make no assumption about how the errors are distributed. The cost of this generality is that intervals are uniform in width across the covariate space. Methods such as `cv+` or `jackknife+` can produce locally adaptive widths at the expense of additional computation.