Fit a nondecreasing calibration mapping with the Pool Adjacent Violators algorithm. First sort calibration pairs by probability. Start with one block per binary label and repeatedly merge adjacent blocks whenever the earlier block mean exceeds the later block mean. Assign each point its final block mean.

This minimizes:

subject to:

Here, $y_i$ is the sorted calibration label and $c_i$ is its fitted value. For each new probability, clamp outside the calibration range and linearly interpolate between neighboring fitted points inside the range. Return a list of calibrated probabilities in the original new-probability order.