14.3 Summary
In this chapter, we present approximate methods designed for situations where the likelihood function does not have a closed-form expression (e.g., ABC and BSL), or where the sample size and parameter space are large (e.g., INLA and VI), making traditional MCMC and importance sampling (IS) methods ineffective. We provide the theoretical foundations and include applications to illustrate the potential of these methods.
Simulation-based algorithms are affected by the curse of dimensionality in the parameter space, while optimization-based approaches typically require the evaluation of likelihood functions. As a result, recent developments, known as hybrid methods, combine these two strategies to address scenarios where both challenges arise simultaneously. See (G. M. Martin, Frazier, and Robert 2024a) for further references on this topic.