A joint rule narrowed alpha difference ranges in ds004148; 95% coverage requires exchangeable person records

We tested joint prediction ranges for closed-eye alpha log power, open-eye alpha log power, and their difference. The data were visits 1 and 3 from 60 adults in OpenNeuro ds004148 version 1.0.1. Each allocation had 20 training, 20 calibration, and 20 test people. One joint rule included the difference in a maximum residual score. A second joint rule calibrated two states and derived the difference range by subtraction. In the fixed split, both rules covered all three values for 19 of 20 test people. Direct calibration reduced the difference width from 24.330 to 20.172 dB, or 17.09%. Across 10,000 random allocations, mean joint coverage was 95.1865% and 95.1580% for the two joint rules, and 89.8000% for three separate 95% rules. Direct difference ranges were narrower in every allocation. Their mean relative width reduction was 23.83%. A proof shows that direct calibration cannot widen the difference range when predictions use the difference identity and its training scale is no greater than the sum of the state scales. State ranges can widen. The rank coverage bound is 20/21 for one future person, conditional on a fixed training fit and exchangeable person records. It is not a guarantee conditional on a baseline value or a fixed calibration set. Exact subset counts gave 20/21 and 90.29% average joint coverage for joint and separate rules with training fixed. These counts describe the recorded cohort. The method uses established split conformal theory. The package preserves 240 spectral files, source hashes, code, proofs, full results, and raw retrieval instructions. Four public raw records rebuilt all arrays with zero error. Independent checks covered all scores and fits. An offline repeat gave identical bytes for 24 numeric result files.

conformal prediction · prediction intervals · EEG · alpha power · exchangeability · joint coverage · test-retest