Probability Calibration for Area Estimation — Interactive Demo

Overview. A probabilistic model assigns each grid cell a probability of being inside a polygon. When the model is miscalibrated (e.g., overconfident or underconfident), summing raw probabilities gives biased area estimates. Calibration corrects these probabilities using a held-out reference sample so that predicted probabilities match observed frequencies.

• Bias model: applies a sigmoid/logit transform with adjustable strength to create miscalibration.
• Isotonic regression (PAVA): non-parametric monotone recalibration — fits a step function to training data.
• Platt scaling: fits a sigmoid (logistic) function σ(Ax + B) via gradient descent to recalibrate predictions.
• Reliability diagram: plots predicted probability vs. observed frequency — perfectly calibrated models lie on the diagonal.
• ECE (Expected Calibration Error) and Brier score quantify calibration quality on the test set.