Point estimates, Simpson's paradox, and nonergodicity in biological sciences

Abstract

Modern biomedical, behavioral and psychological inference about cause-effect relationships respects an ergodic assumption, that is, that mean response of representative samples allow predictions about individual members of those samples. Recent empirical evidence in all of the same fields indicates systematic violations of the ergodic assumption. Indeed, violation of ergodicity in biomedical, behavioral and psychological causes is precisely the inspiration behind our research inquiry. Here, we review the long term costs to scientific progress in these domains and a practical way forward. Specifically, we advocate using statistical measures that can themselves encode the degree and type of nonergodicity in measurements. Taking such steps will lead to a paradigm shift, allowing researchers to investigate the nonstationary, far-from-equilibrium processes that characterize the creativity and emergence of biological and psychological behavior.

Keywords: Ergodic; Longitudinal modeling; Nonergodic; Stationarity; Statistical analysis; Vector autoregression.