Using Bayesian dynamical systems, model averaging and neural networks to determine interactions between socio-economic indicators

Abstract

Social and economic systems produce complex and nonlinear relationships in the indicator variables that describe them. We present a Bayesian methodology to analyze the dynamical relationships between indicator variables by identifying the nonlinear functions that best describe their interactions. We search for the ‘best’ explicit functions by fitting data using Bayesian linear regression on a vast number of models and then comparing their Bayes factors. The model with the highest Bayes factor, having the best trade-off between explanatory power and interpretability, is chosen as the ‘best’ model. To be able to compare a vast number of models, we use conjugate priors, resulting in fast computation times. We check the robustness of our approach by comparison with more prediction oriented approaches such as model averaging and neural networks. Our modelling approach is illustrated using the classical example of how democracy and economic growth relate to each other. We find that the best dynamical model for democracy suggests that long term democratic increase is only possible if the economic situation gets better. No robust model explaining economic development using these two variables was found.

Coupling functions: dynamical interaction mechanisms in the physical, biological and social sciences

“…In biology the new methods have been applied to characterize genetic oscillators and homogeneous flocking [51,52], and in cardiorespiratory physiology they have been used for reconstruction of the human cardiorespiratory coupling function and phase resetting curve [35,36,59,62]. In social sciences, the function underlying the interactions between different social and economic dynamical dependences has been determined [50,51,60]. The mechanical coupling functions between coupled metronomes were reconstructed in a similar way [47].…”

“…Applications have now been reported in, for example: chemistry, neuroscience, cardiorespiratory physiology, biology, social sciences, mechanics, ferromagnetism, secure encryption and ecology [28,32,[35][36][37]46,47,[50][51][52][53][54][55][56][57][58][59][60][61]. In chemistry, coupling function methods have been used for understanding, effecting, and predicting interactions between oscillatory electrochemical reactions [28,32,37,56,57].…”

Synchronization transitions caused by time-varying coupling functions

“…Many dynamical systems, both natural and man-made, are composed of interacting parts. Examples include Josephson junctions [1,2], neuronal networks [3][4][5], the cardiorespiratory system [6][7][8], cardiorespiratory-brain interactions [9][10][11][12], and systems occurring in social sciences [13,14], communications [15,16] and chemistry [17][18][19]. Such systems often have external influences leading to time-variability in their mathematical description, e.g.…”

Inferring the dynamics of rising radical right-wing party support using Gaussian processes

“…changes over time), rather than stock values. A dynamical systems approach uses a nonlinear differential or difference equation to describe the rate of change of each variable in a social system in terms of itself and other social variables [34][35][36][37]. For example, the rate of change in RRP support can be fitted as a function of education, unemployment, immigration and so on.…”