Warped Bayesian linear regression for normative modelling of big data

•We present a warped Bayesian Linear Regression (BLR) and demonstrate it on data from the UK Biobank.•The non-linearity of the model improves the fit and out of sample predictions for most variables.•Non-Gaussianity of the data can be included with the incorporation of the likelihood warping.•A trade-off between fit and complexity can be chosen optimally, without crossvalidation.•BLR is computationally less demanding than GPR and is therefore scalable to big datasets.