Mechanistic simulations are used to model complex systems in research fields such as genetics, epidemiology, and cosmology to name few, for which explicit statistical models are challenging to express. In such simulator-based models, synthetic data are generated to represent the underlying real-world phenomena of interest based on our mechanistic understanding of the system. Unfortunately, standard statistical inference methods are poorly suited to simulator-based models, as their likelihood function-a quantity central to both frequentist and Bayesian inference ―is typically intractable. To address this issue, a host of simulation-based inference (SBI) methods have been developed that circumvent the need to evaluate the likelihood or its derivatives by relying on forward simulations from the model. SBI methods permit sampling from an approximate posterior by either comparing distances between simulated and observed datasets (or their respective summary statistics) or by training a conditional density estimator, typically a neural network, to approximate the relevant probability distribution. SBI methods have led to significant advances in many scientific disciplines. SBI methods implicitly assume that the simulator accurately represents the true data-generating process and that generating large amounts of synthetic data from the simulator is straightforward. However, these assumptions are often not met in practice, as simulators tend to be (i) misspecified, meaning that the true data distribution does not lie within the parametric family of distributions defined by the simulator, for example due to outliers, and (ii) computationally expensive to run, making it difficult for existing SBI methods to produce trustworthy posterior samples. This PhD project will develop SBI methods that remain trustworthy when simulations are misspecified or computationally expensive.
