Continuous Probabilistic Forecasts#
Forecasts expressed as continuous probability distributions over outcomes.
Important
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What it is#
A continuous probabilistic forecast is a probabilistic forecast for a continuous (real-valued) outcome — a full predictive distribution over the variable (a density or CDF), rather than a single value or a class probability. It answers what is the whole distribution of tomorrow’s demand, price, or temperature?
How it’s represented#
It can be given as a parametric distribution (e.g. a normal \(\mathcal{N}(\mu, \sigma^2)\) with a forecast mean and variance), a set of quantiles, or an ensemble of sampled trajectories — each a way to describe the continuous outcome’s uncertainty.
Why it’s useful#
From one object it exposes every downstream quantity — the mean, any quantile, a prediction interval, or a tail probability. Because it lives on a continuum (unlike a discrete / categorical probabilistic forecast), it is scored with the CRPS.
Theme: Risk & Probabilistic Forecasting · All terminology
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Mind map — connected ideas
Probabilistic Forecasts · Full Distribution · Probabilistic Scoring · Strictly Proper Scoring Rules · Quantile Forecasts · Prediction Intervals (PI)
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More in Risk & Probabilistic Forecasting
Continuous Ranked Probability Score (CRPS) · Deterministic forecasts · Full Distribution · Pinball Loss (a.k.a. Quantile Loss) · Point Forecasts · Predicting Percentiles · Prediction Intervals (PI) · Probabilistic Forecasts · Probabilistic Scoring · Probability Forecasts · Quantile Forecasts · Quantile Level · Quantile Regression · Return Distribution
See also
Source article Adapted (context, re-expressed) in our own words from: Continuous Probabilistic Forecasts (insightful-data-lab.com).