Bayesian Gaussian Processes. Or: How I Learned to Stop Worrying and Love Nonlinear Social Science

Nonlinearity is ubiquitous in the social sciences.

In cross-sectional research, nonlinearity naturally follows from the fact that variables often depend on human perception.

The tendency to share fake news, for example, depends in a complex nonlinear manner on peoples’ personality and political preferences.

In longitudinal research, nonlinearity follows from the fact that temporal social processes are nonstationary by nature.

For instance, stressful life events (e.g., unemployment, pandemic) have a complex nonlinear impact on well-being over time. To study these nonlinear phenomena, much more data are needed than in linear analyses.

Therefore, researchers increasingly rely on technological innovations to collect rich data, such as panel data via online surveys, experience sampling data via mobile apps, or temporal social network data using digital communication (e.g., email). In addition, prior information (e.g., from experts) is often available to inform us about plausible nonlinear shapes.

A crucial problem is however that statistical approaches for learning nonlinearity still heavily rely on old-fashioned techniques which can only model simple (curvilinear) effects and are unable to include external prior information. Our understanding about nonlinear phenomena therefore remains limited.

This project aims to resolve these shortcomings by developing cutting-edge methods for nonlinear social science using Bayesian Gaussian processes.

With this nonparametric methodology, we can learn complex nonlinear shapes, add prior knowledge, and test nonlinear theories. Implementation in user-friendly software will ensure general utilization.

Tailor-made extensions will be developed for cross-sectional data, panel data, experience sampling data, and temporal social network data.

After this project, we will be able to truly understand complex nonlinear mechanisms, to learn how these unfold over time, and to make accurate predictions (e.g., of well-being after life events).