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Forecast Quantile
Predicted value corresponding to a specific percentile of the forecast distribution, allowing characterization of optimistic, pessimistic, or median scenarios with an associated probability.
Forecast Distribution
Complete mathematical representation of the probability of each possible future outcome, forming the basis of all probabilistic analysis and risk quantification.
Quantile Function
Inverse function of the cumulative distribution function, which for a given probability p, returns the value x such that the probability of a random variable being less than or equal to x equals p.
Pinball Score
Evaluation metric specifically designed for quantile forecasts, which penalizes predictions asymmetrically depending on whether the predicted quantile is above or below the observed value.
Ensemble Forecast
Probabilistic method that generates a collection of forecasts by varying initial conditions, model parameters, or model structure to approximate the forecast distribution.
Residual Bootstrapping
Resampling technique that involves randomly drawing with replacement from the residuals of a fitted model to simulate many future scenarios and build an empirical forecast distribution.
Bayesian Forecasting
Probabilistic forecasting framework that updates beliefs about model parameters and future forecasts by combining a prior distribution with the likelihood of observed data to obtain a posterior distribution.
Fan Chart
Graphical visualization of probabilistic forecasts that displays a series of prediction intervals (e.g., 50%, 80%, 95%) to show how uncertainty increases with the time horizon.
Scenario Forecasting
Generation of multiple possible future evolution paths, each with a probability, to explore a range of outcomes and facilitate strategic planning under uncertainty.
Quantile Regression (QR) Method
Modeling technique that directly estimates conditional quantiles of the response variable, allowing construction of the complete forecast distribution without assuming a specific error distribution.
Forecast Density
Probability density function that describes the relative likelihood of all possible values for a future variable at a specific point in time, providing the most complete representation of uncertainty.
Continuous Ranked Probability Score (CRPS)
Evaluation metric that measures the distance between the cumulative forecast distribution and the observed value, penalizing both inaccuracy and unreliability of probabilistic forecasts.
Monte Carlo Simulation
Computational method using repeated random sampling to calculate a forecast distribution, particularly useful when analytical models are too complex for direct resolution.
Conformal Prediction
Framework that transforms point predictions from a base model into distributionally valid set forecasts, guaranteeing that interval coverage is close to the nominal confidence level.