Agent-based model calibration using likelihood-free inference

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It is often possible to design simulators that are capable of modelling complex phenomena but are not well suited to standard statistical methods. This arises when running the simulator is straightforward, but the corresponding likelihood function is intractable, often due to a large number of latent variables which would need to be marginalised over to obtain the likelihood function. One key example are agent-based models, a flexible class of models where the behaviours of individual agents are specified, which then interact often producing complex emergent behaviour.Recently, many simulation-based inference methods have been developed, which use simulations to approximate a function of interest, for example the likelihood, the posterior, or the likelihood-to-evidence ratio. Often the raw simulator output is of too high dimension to be used directly, so inference is instead performed using a set of summary statistics. In most models of interest, the simulator will be somewhat misspecified, meaning that the simulator does not perfectly replicate the true underlying data generating process (for any set of parameters). This leads to issues when approximating the function of interest, for example when approximating the likelihood, the observed data (or summary statistics) may fall far in the tails of the likelihood where density estimation may be unreliable, particularly for powerful methods like normalising flows (Papamakarios et al., 2021). The difficulty of handling misspecification in a principled manner has hindered application of simulators and simulation-based methods.The overall aim of the project is to contribute to simulation-based methods and investigate ways to improve their robustness to model misspecification. Currently, this project will focus on two areas. The first focus of the project is to investigate the use of gradient boosting for obtaining conditional density estimates (e.g. the likelihood; Thomas et al., 2018). Gradient boosting is a method for constructing ensemble models from a set of simple base learning algorithms. A particular advantage of using a boosting framework is that variable selection and model fitting can be performed jointly. In the context of likelihood approximation, this corresponds to automatically selecting simulator parameters used to predict the conditional distribution parameters. The second area of investigation will be to develop methods for learning summary statistics that are informative and robust to misspecification. One option to achieve this could be to use variational autoencoders, which have been widely used to learn low dimensional representations of datasets in machine learning. To improve robustness to misspecification, ideas from generalised Bayesian posteriors (Schmon et al., 2020) or semi-modular inference (Carmona and Nicholls, 2020) could be applied to adapt the objective function.