Scientists and engineers use simulators to model empirically observed phenomena. However, tuning the parameters of a simulator to ensure its outputs match observed data presents a significant challenge. Simulation-based inference (SBI) addresses this by enabling Bayesian inference for simulators, identifying parameters that match observed data and align with prior knowledge. Unlike traditional Bayesian inference, SBI only needs access to simulations from the model and does not require evaluations of the likelihood-function. In addition, SBI algorithms do not require gradients through the simulator, allow for massive parallelization of simulations, and can perform inference for different observations without further simulations or training, thereby amortizing inference. Over the past years, we have developed, maintained, and extended $\texttt{sbi}$, a PyTorch-based package that implements Bayesian SBI algorithms based on neural networks. The $\texttt{sbi}$ toolkit implements a wide range of inference methods, neural network architectures, sampling methods, and diagnostic tools. In addition, it provides well-tested default settings but also offers flexibility to fully customize every step of the simulation-based inference workflow. Taken together, the $\texttt{sbi}$ toolkit enables scientists and engineers to apply state-of-the-art SBI methods to black-box simulators, opening up new possibilities for aligning simulations with empirically observed data.

Computational models are invaluable in capturing the complexities of real-world biological processes. Yet, the selection of appropriate algorithms for inference tasks, especially when dealing with real-world observational data, remains a challenging and underexplored area. This gap has spurred the development of various parameter estimation algorithms, particularly within the realm of Simulation-Based Inference (SBI), such as neural and statistical SBI methods. Limited research exists on how to make informed choices on SBI methods when faced with real-world data, which often results in some form of model misspecification. In this paper, we provide comprehensive guidelines for deciding between SBI approaches for complex biological models. We apply the guidelines to two agent-based models that describe cellular dynamics using real-world data. Our study unveils a critical insight: while neural SBI methods demand significantly fewer simulations for inference results, they tend to yield biased estimations, a trend persistent even with robust variants of these algorithms. On the other hand, the accuracy of statistical SBI methods enhances substantially as the number of simulations increases. This finding suggests that, given a sufficient computational budget, statistical SBI can surpass neural SBI in performance. Our results not only shed light on the efficacy of different SBI methodologies in real-world scenarios but also suggest potential avenues for enhancing neural SBI approaches. This study is poised to be a useful resource for computational biologists navigating the intricate landscape of SBI in biological modeling.

Simulation-based inference (SBI) refers to statistical inference on stochastic models for which we can generate samples, but not compute likelihoods. Like SBI algorithms, generative adversarial networks (GANs) do not require explicit likelihoods. We study the relationship between SBI and GANs, and introduce GATSBI, an adversarial approach to SBI. GATSBI reformulates the variational objective in an adversarial setting to learn implicit posterior distributions. Inference with GATSBI is amortised across observations, works in high-dimensional posterior spaces and supports implicit priors. We evaluate GATSBI on two SBI benchmark problems and on two high-dimensional simulators. On a model for wave propagation on the surface of a shallow water body, we show that GATSBI can return well-calibrated posterior estimates even in high dimensions. On a model of camera optics, it infers a high-dimensional posterior given an implicit prior, and performs better than a state-of-the-art SBI approach. We also show how GATSBI can be extended to perform sequential posterior estimation to focus on individual observations. Overall, GATSBI opens up opportunities for leveraging advances in GANs to perform Bayesian inference on high-dimensional simulation-based models.