Glossary¶

This glossary defines key terms and concepts used throughout the k-diagram documentation and package.

ACF (Autocorrelation Function)¶

A function that measures the correlation between a time series and its own past values at different time lags. Used by plot_error_autocorrelation() to check for remaining patterns in forecast errors.

ACov (Angular Coverage)¶

A parameter (acov) controlling the angular span of the polar plots, such as ‘default’ (360°), ‘half_circle’ (180°), ‘quarter_circle’ (90°), or ‘eighth_circle’ (45°).

Anomaly (Prediction)¶

An instance where the observed (actual) value falls outside the predicted uncertainty interval (i.e., below Qlow or above Qup). Visualized by plot_anomaly_magnitude().

Anomaly Magnitude¶

The severity of a prediction anomaly, measured as the absolute distance between the actual value and the nearest violated prediction interval bound.

AUC (Area Under the Curve)¶

A summary metric for the ROC curve, representing a model’s overall ability to discriminate between positive and negative classes. A higher AUC is better.

Calibration (Interval)¶

The degree to which the empirical coverage rate of prediction intervals matches their nominal coverage rate. A well-calibrated 90% interval should cover approximately 90% of the actual values. is “honest” about its own uncertainty. Assessed by plots like the plot_pit_histogram() and plot_polar_reliability().

Conditional Bias¶

A systemic error where a model’s bias (the tendency to over- or under-predict) changes depending on the value of another variable, such as the true value or the predicted value itself. Diagnosed by plot_error_relationship().

Confusion Matrix¶

A table used to evaluate the performance of a classification model. It summarizes the counts of True Positives (TP), False Positives (FP), True Negatives (TN), and False Negatives (FN). Visualized by plot_polar_confusion_matrix().

Consistency (Interval Width)¶

The stability or variability of the prediction interval width (Qup - Qlow) for a specific location or sample across multiple time steps or forecast horizons. Assessed by plot_interval_consistency().

Coverage (Empirical)¶

The actual fraction or percentage of observed (true) values that fall within their corresponding prediction intervals in a given dataset. Calculated by plot_coverage() and visualized point-wise by plot_coverage_diagnostic().

Coverage (Nominal)¶

The theoretical or intended coverage rate of a prediction interval, determined by the quantile levels used. For example, the interval between the 10th (Q10) and 90th (Q90) percentiles has a nominal coverage of 80%.

Drift (Model / Concept)¶

The degradation or change in a model’s performance or underlying data relationships over time or changing conditions.

Drift (Uncertainty)¶

The change in the magnitude or pattern of predicted uncertainty (typically interval width) over time or forecast horizons. Visualized by plot_model_drift() (average drift) and plot_uncertainty_drift() (pattern drift).

F1-Score¶

A classification metric that calculates the harmonic mean of Precision and Recall. It provides a single score that balances both metrics, and is particularly useful for imbalanced datasets.

Fingerprint (Feature)¶

A characteristic profile of feature importance values for a specific model, time period, or group, often visualized using a radar chart via plot_feature_fingerprint().

Forecast Horizon¶

The number of time steps into the future for which a forecast is made. A “multi-horizon” forecast provides predictions for multiple future time steps simultaneously.

Forecasting¶

The process of making predictions about future events based on past and present data. This typically involves analyzing time series data to identify patterns and project them forward.

Heteroscedasticity¶

A condition where the variance of a model’s errors is not constant. Diagnosed by plots like plot_conditional_quantiles() and plot_residual_relationship().

Interval Width¶

The difference between the upper quantile (Qup) and lower quantile (Qlow) of a prediction interval, representing the magnitude of predicted uncertainty. Visualized by plot_interval_width().

K-Diagram¶

The term used for the specialized polar diagnostic plots generated by this package, named after the author (Kouadio).

Lag¶

In time series analysis, the time difference or number of time steps between an observation and a previous observation. Used in ACF and PACF plots to measure autocorrelation at different past intervals.

PACF (Partial Autocorrelation Function)¶

A function that measures the direct correlation between a time series and a lagged version of itself, after removing the influence of shorter lags. Used by plot_error_pacf().

Pinball Loss¶

A metric used to evaluate the accuracy of a single quantile forecast. The CRPS is the average of the Pinball Loss over all quantiles. Visualized by plot_pinball_loss().

PIT (Probability Integral Transform)¶

A method for evaluating the calibration of a probabilistic forecast. For a well-calibrated model, the PIT values of the observations should be uniformly distributed. Visualized by plot_pit_histogram().

Point Forecast¶

A single-value prediction of a future outcome, typically the mean or median of the forecast distribution. Contrasts with a probabilistic forecast.

Polar Plot / Coordinates¶

A graphical system where points are located by an angle (theta, θ) and a distance from a central point (radius, r). Used extensively in k-diagram.

Precision¶

A classification metric that measures the accuracy of positive predictions. Defined as \(TP / (TP + FP)\).

Prediction Interval (PI)¶

A range [Qlow, Qup] derived from quantile forecasts, intended to contain the actual observed value with a certain probability (nominal coverage).

Probabilistic Forecast¶

A forecast that provides a full probability distribution for a future outcome, rather than just a single point value. This is often represented by a set of quantiles.

Proper Scoring Rule¶

A metric used to evaluate the quality of a probabilistic forecast that simultaneously assesses both calibration and sharpness. A key property is that the forecaster is incentivized to report their true belief to get the best score. The CRPS and Winkler Score are examples.

Q-Q Plot (Quantile-Quantile Plot)¶

A plot that compares the quantiles of a sample distribution (e.g., forecast errors) against the quantiles of a theoretical distribution (e.g., normal) to check for similarity.

Quantile¶

A value below which a certain proportion of the data or probability distribution falls. Common examples used in forecasting are Q10 (10th percentile), Q50 (50th percentile or median), and Q90 (90th percentile).

Radar Chart¶

A type of polar plot where multiple quantitative variables (represented by axes radiating from the center) are shown for one or more observations (represented by polygons or lines). Used by plot_feature_fingerprint() and optionally by plot_coverage().

Recall (Sensitivity)¶

A classification metric that measures the ability of a model to find all the actual positive samples. Defined as TP / (TP + FN).

Reliability Diagram¶

A plot that compares predicted probabilities to observed frequencies to assess a classifier’s calibration.

Residual¶

Another term for forecast error, calculated as the difference between the actual observed value and the model’s predicted value (\(e_i = y_{true,i} - y_{pred,i}\)).

RMSD (Centered Root Mean Square Difference)¶

A metric implicitly represented on a Taylor Diagram as the distance between a model point and the reference point. It measures the overall difference considering both standard deviation and correlation.

ROC Curve (Receiver Operating Characteristic Curve)¶

A plot that shows the performance of a binary classifier by plotting the True Positive Rate against the False Positive Rate.

Sharpness¶

A measure of the concentration or narrowness of a probabilistic forecast’s distribution, typically quantified by the average prediction interval width. A sharper forecast is more precise. Visualized by plot_polar_sharpness().

Taylor Diagram¶

A polar-style diagram summarizing model skill by plotting standard deviation (radius), correlation (angle), and RMSD (distance from reference) relative to observed data. Generated by functions in kdiagram.plot.evaluation.

Tidy Data¶

A standard for structuring datasets where each row is an observation, each column is a variable, and each table represents a single observational unit. The reshaping utilities in kdiagram.utils.q_utils are designed to help create tidy data.

Uncertainty Quantification (UQ)¶

The process of estimating and characterizing the uncertainty associated with model predictions, simulations, or measurements.

A rigorous framework for identifying, characterizing, and managing the uncertainty inherent in computational models and predictions. UQ moves beyond single point forecasts to provide a probabilistic view of all possible outcomes. It aims to distinguish between two primary sources of uncertainty:

Aleatoric uncertainty: The inherent randomness or variability in a system that cannot be reduced with more data (e.g., the roll of a die).
Epistemic uncertainty: Uncertainty due to a lack of knowledge, such as imperfect model parameters or structure. This type of uncertainty can potentially be reduced with more data or better models.

The ultimate goal of UQ is to produce a probabilistic forecast that is both calibrated (reliable) and sharp (precise). The tools in k-diagram are designed to visually diagnose the quality of these UQ efforts.

Velocity (Prediction)¶

The average rate of change of the central prediction estimate (e.g., Q50) over consecutive time steps for a given location or sample. Visualized by plot_velocity().

Winkler Score¶

A proper scoring rule for evaluating a prediction interval that rewards sharpness (narrow intervals) while penalizing for a lack of coverage.