# Gaussian Process Regression

Brain-age models trained mostly on Global North data lose accuracy when applied to Nigerian adults. A population-specific Gaussian process regression model trained on clinical T1-weighted MRI from 309 Nigerian adults reached a mean absolute error of 9.82 years on a 47-participant held-out test set without age-bias correction; on the 44-participant head-to-head set it reached 10.24 years, against 10.52 years for PyBrainAge, 12.33 for SynthBA, 17.51 for ENIGMA-Brain Age and 7.87 for SPARROW. After correction it reached 6.39 years internally but 8.78 years on a separate Nigerian cohort, where every model's R2 was negative.

Brain-age models trained mostly on Global North data lose accuracy when applied to Nigerian adults. A population-specific Gaussian process regression model trained on clinical T1-weighted MRI from 309 Nigerian adults reached a mean absolute error of 9.82 years on a 47-participant held-out test set without age-bias correction; on the 44-participant head-to-head set it reached 10.24 years, against 10.52 years for PyBrainAge, 12.33 for SynthBA, 17.51 for ENIGMA-Brain Age and 7.87 for SPARROW. After correction it reached 6.39 years internally but 8.78 years on a separate Nigerian cohort, where every model's R2 was negative.

Galaxy rotation curves have long favored cored dark-matter halos over the steeply rising cusps predicted by cold dark matter simulations. Fitting five SPARC galaxies with Bayesian inference while modeling correlated errors between neighboring radii largely closes that gap. In DDO 154 the reduced chi-square moves from 2.40 versus 9.41 to 0.94 versus 1.04, leaving one-dimensional rotation curves unable to separate the two halo shapes.

Galaxy rotation curves have long favored cored dark-matter halos over the steeply rising cusps predicted by cold dark matter simulations. Fitting five SPARC galaxies with Bayesian inference while modeling correlated errors between neighboring radii largely closes that gap. In DDO 154 the reduced chi-square moves from 2.40 versus 9.41 to 0.94 versus 1.04, leaving one-dimensional rotation curves unable to separate the two halo shapes.

Optimizing biomass torrefaction experimentally is limited by cost and time, since one-factor-at-a-time trials miss synergistic effects and full factorial designs quickly become prohibitive. Using 486 torrefaction observations, Gaussian process regression with automatic relevance determination kernels reached cross-validated R² of 0.854 for mass yield, 0.971 for higher heating value and 0.869 for energy yield, outperforming random forest, support vector regression and a neural network. An acquisition function weighting uncertainty, mass-yield improvement and HHV improvement at 0.4/0.3/0.3, plus a diversity penalty, then recommended 10 experiments spanning 200–315 °C and 30–1089 s, all inside the conventional torrefaction window.

Optimizing biomass torrefaction experimentally is limited by cost and time, since one-factor-at-a-time trials miss synergistic effects and full factorial designs quickly become prohibitive. Using 486 torrefaction observations, Gaussian process regression with automatic relevance determination kernels reached cross-validated R² of 0.854 for mass yield, 0.971 for higher heating value and 0.869 for energy yield, outperforming random forest, support vector regression and a neural network. An acquisition function weighting uncertainty, mass-yield improvement and HHV improvement at 0.4/0.3/0.3, plus a diversity penalty, then recommended 10 experiments spanning 200–315 °C and 30–1089 s, all inside the conventional torrefaction window.