Structural and parametric uncertainties in full Bayesian and graphical lasso based approaches: Beyond edge weights in psychological networks

Abstract

Uncertainty over model structures poses a challenge for many approaches exploring effect strength parameters at system-level. Monte Carlo methods for full Bayesian model averaging over model structures require considerable computational resources, whereas bootstrapped graphical lasso and its approximations offer scalable alternatives with lower complexity. Although the computational efficiency of graphical lasso based approaches has prompted growing number of applications, the restrictive assumptions of this approach are frequently ignored. We demonstrate using an artificial and a real-world example that full Bayesian averaging using Bayesian networks provides detailed estimates through posterior distributions for structural and parametric uncertainties and it is a feasible alternative, which is routinely applicable in mid-sized biomedical problems with hundreds of variables. We compare Bayesian estimates with corresponding frequentist quantities from bootstrapped graphical lasso using pairwise Markov Random Fields, discussing also their different interpretations. We present results using synthetic data from an artificial model and using the UK Biobank data set to construct a psychopathological network centered around depression (this research has been conducted using the UK Biobank Resource under Application Number 1602).