From agent-based models to statistical emulators
Jakub Bijak, Jason Hilton and Eric Silverman
University of Southampton, Southampton, SO17 1BJ, United Kingdom
Contact author: firstname.lastname@example.org
Proposed for the strand on «New methodologies» Eurostat / UNECE Work Session on Population Projections; Rome, 29–31 October 2013
Contemporary demographic micro-simulations are largely concerned with populations of statistical individuals, whose life courses can be inferred from empirical information (Courgeau 2012). In contrast, agent-based models study simulated individuals, for whom certain behavioural rules are assumed. We wish to bring these two approaches closer together by coupling the rule-based explanations driving the agent-based model with observed data. We also propose a method to analyse the statistical properties of such models, based on the notion of statistical emulators (Kennedy & O’Hagan 2001; Oakley & O’Hagan 2002).
In this paper, we present a Semi-Artificial Model of Population, which aims to bridge demographic micro-simulation and agent-based traditions. We extend the ‘Wedding Ring’ agent-based model of marriage formation (Billari et al. 2007) to include empirical information on the natural population change for the United Kingdom alongside with the behavioural explanations that drive the observed demographic trends. The mortality and fertility rates in this population are drawn from UK population data for 1951–2011 and forecasts until 2250 obtained from Lee-Carter models. We then utilise a Gaussian process emulator – a statistical model of the base model – to analyse the impact of selected parameters on two key simulation outputs: population size and share of agents with partners. A sensitivity analysis is attempted, aiming to assess the relative importance of different inputs.
The resulting multi-state model of population dynamics is argued to have enhanced predictive capacity as compared to the original specification of the Wedding Ring, but there are some trade-offs between the outputs considered. The sensitivity analysis indicates a key role of social pressure in the modelled partnership formation process. We posit that the presented method allows for generating coherent, multi-level agent-based scenarios aligned with selected aspects of empirical demographic reality. Emulators permit a statistical analysis of the model properties and help select plausible parameter values. Given non-linearities in agent-based models such as the Wedding Ring, and the presence of feedback loops, the uncertainty of the model may be impossible to assess directly with traditional statistical methods. The use of statistical emulators offers a way forward.
Billari, F., Aparicio Diaz, B., Fent, T. and Prskawetz, A. (2007) The “Wedding–Ring”. An agent–based marriage model based on social interaction. Demographic Research, 17(3): 59–82.
Courgeau, D. (2012). Probability and Social Science. Methodological Relationships between the two Approaches. Dordrecht: Springer.
Kennedy, M., and O’Hagan, T. (2001) Bayesian Calibration of Computer Models. Journal of the Royal Statistical Society, Series B, 63(3), pp. 425–464.
Oakley, J. and O’Hagan, A. (2002) Bayesian inference for the uncertainty distribution of computer model outputs. Biometrika, 89(4), pp. 769–784.