Posterior estimation of longitudinal variance components from nonlongitudinal data using Bayesian Gaussian process model.

Many quantitative traits can be measured from a single individual only once, making acquisition of longitudinal data impossible. In this paper, we present Gaussian process restricted Bayesian estimation, a new method tailored for estimating posterior distributions of longitudinal variance components from data where each individual contributes only 1 measurement at a single time point to the study. However, by collecting all time points together, one can think data to be longitudinal at the population level which makes it possible to estimate longitudinal variance components. The method can be also applied for reaction norm problems where it is common that a value of continuous environmental condition (e.g. temperature) is measured only once per individual. The work is based on Bayesian framework, Markov chain Monte Carlo estimation, and assuming Gaussian process-based smoothing priors for the variance components. The performance of the method is illustrated with simulated and real data sets as well as compared with a random regression model. Our method is very stable and it is flexible in handling any kind of smooth curves. Uncertainty around the variance curves is represented with 95% credible interval curves computed from the posterior distribution. The code is available at the GitHub repository https://github.com/aarjas/GP-REBE.