# Inference for a complex world

What is ABC? In the world of statistics, it stands for Approximate Bayesian Computation. ACEMS' research assistant Abhishek Vargese recently completed an AMSI Vacation Research Experience Scheme (VRES) and wrote this blog about what he learned about ABC:

A quick glance at the United Nations list of global issues shows us the myriad of complex and diverse challenges we face today [1]. Mathematical modelling is an excellent tool for enabling us to understand and solve these challenges. With data availability and computational resources rapidly increasing, our models are growing in increasing complexity to match the grand scale of these global issues. However, this introduces significant challenges in accurately calibrating these complex models to precisely emulate the interactions we observe in the real world.

Complex models are often hard to express as a formula, making it impossible to use classical statistical methods to accurately calibrate the model.

Enter approximate Bayesian computation (ABC).

Also known as simulator-based inference, ABC is a class of statistical methods that test a wide range of possible model parameters and compare the resulting output to the observed data. ABC identifies model parameters that consistently provide model results that match the real dataset closely. Thus, ABC enables relatively accurate calibration in scenarios where it was not possible before!

ABC has been used in a variety of applications. It is widely used for applications in biological sciences e.g., in population genetics, ecology, epidemiology, and systems biology[2]. Recently, ABC has been essential in calibrating models to forecast and predict COVID-19 outbreaks in countries[3], or to describe the spread of diseases in a plantation[4]. ABC has helped evaluate energy policy, by enabling a complex Agent-Based Model to accurately forecast the fiscal effects of different feed-in tariff structures in Great Britain[5].  Although airline travel is still limited today, ABC has enabled us to use a complex queuing system to accurately model the foot traffic flow in airports[6].

These are just a few examples where ABC has proven to be invaluable in calibrating models to aid in understanding and solving large problems. The idea behind ABC is intuitive, and effectively leverages the rapid increase in computational power and the availability of large datasets to model processes previously beyond reach. Among many other instruments in a statistician’s toolkit, ABC can help us stand tall when faced with the Goliath-like issues we are surrounded by today and tackle them with greater precision!

References

• [1] ‘Global Issues Overview’, Nov. 19, 2015. https://www.un.org/en/sections/issues-depth/global-issues-overview/ (accessed Feb. 18, 2021).
• [2] J. S. Lopes and M. A. Beaumont, ‘ABC: a useful Bayesian tool for the analysis of population data’, Infect. Genet. Evol., vol. 10, no. 6, pp. 825–832, 2010.
• [3] D. J. Warne, A. Ebert, C. Drovandi, W. Hu, A. Mira, and K. Mengersen, ‘Hindsight is 2020 vision: a characterisation of the global response to the COVID-19 pandemic’, BMC Public Health, vol. 20, no. 1, pp. 1–14, 2020.
• [4] A. Varghese, C. Drovandi, A. Mira, and K. Mengersen, ‘Estimating a novel stochastic model for within-field disease dynamics of banana bunchy top virus via approximate Bayesian computation’, PLOS Comput. Biol., vol. 16, no. 5, pp. 1–23, 2020, doi: 10.1371/journal.pcbi.1007878.
• [5] P. Pearce and R. Slade, ‘Feed-in tariffs for solar microgeneration: Policy evaluation and capacity projections using a realistic agent-based model’, Energy Policy, vol. 116, pp. 95–111, 2018.
• [6] A. Ebert, P. Wu, K. Mengersen, and F. Ruggeri, ‘Computationally efficient simulation of queues: the R package queuecomputer’, ArXiv Prepr. ArXiv170302151, 2017.