Produces a compositional prediction region that respects the simplex constraint (frequencies sum to 1) using Aitchison geometry. Unlike marginal conformal prediction, joint prediction guarantees that the entire frequency vector is covered, not just individual lineages.
Usage
conformal_forecast_joint(
fit,
data,
horizon = 28L,
ci_level = 0.95,
cal_fraction = 0.3,
seed = NULL
)Arguments
- fit
An
lfq_fitobject.- data
An
lfq_dataobject (same data used to fit the model).- horizon
Integer; forecast horizon in days (default 28).
- ci_level
Numeric in (0,1); coverage target (default 0.95).
- cal_fraction
Numeric in (0,1); fraction of dates for calibration (default 0.3).
- seed
Optional integer for reproducibility.
Value
An lfq_conformal_joint S3 object (list) with:
- forecast
The point forecast (
lfq_forecast).- radius
Conformal radius in Aitchison distance.
- marginal_intervals
Tibble with .date, .lineage, .lower_joint, .upper_joint — marginal bounds projected from the joint region.
- marginal_only
Tibble with .lower_marginal, .upper_marginal from standard marginal conformal prediction.
- comparison
Tibble indicating whether joint intervals are wider or narrower than marginal intervals per lineage.
- calibration_scores
Aitchison distances on calibration set.
- ci_level
Nominal coverage level.
- n_cal
Number of calibration compositions.
Details
The nonconformity score is the Aitchison distance between predicted and observed compositions. The Aitchison distance equals the Euclidean distance in the isometric log-ratio (ILR) transformed space, which respects the geometry of the simplex (Aitchison, 1986).
The prediction region is the set of all compositions within Aitchison distance \(r\) of the point forecast, where \(r\) is the \((1-\alpha)(1+1/n)\) quantile of calibration distances. Marginal intervals are obtained by projecting this region onto each coordinate axis, then intersecting with \([0, 1]\).