Inferring parameters of computational models that capture experimental data are a central task in cognitive neuroscience. Bayesian statistical inference methods usually require the ability to evaluate the likelihood of the model—however, for many models of interest in cognitive neuroscience, the associated likelihoods cannot be computed efficiently. Simulation-based inference (SBI) offers a solution to this problem by only requiring access to simulations produced by the model. Previously, Fengler et al. introduced likelihood approximation networks (LANs, Fengler et al., 2021) which make it possible to apply SBI to models of decision-making, but require billions of simulations for training. Here, we provide a new SBI method that is substantially more simulation efficient. Our approach, mixed neural likelihood estimation (MNLE), trains neural density estimators on model simulations to emulate the simulator, and is designed to capture both the continuous (e.g., reaction times) and discrete (choices) data of decision-making models. The likelihoods of the emulator can then be used to perform Bayesian parameter inference on experimental data using standard approximate inference methods like Markov Chain Monte Carlo sampling. We demonstrate MNLE on two variants of the drift-diffusion model and show that it is substantially more efficient than LANs: MNLE achieves similar likelihood accuracy with six orders of magnitude fewer training simulations, and is significantly more accurate than LANs when both are trained with the same budget. Our approach enables researchers to perform SBI on custom-tailored models of decision-making, leading to fast iteration of model design for scientific discovery.

The maintenance of items in working memory (WM) relies on a widespread network of cortical areas and hippocampus where synchronization between electrophysiological recordings reflects functional coupling. We investigated the direction of information flow between auditory cortex and hippocampus while participants heard and then mentally replayed strings of letters in WM by activating their phonological loop. We recorded local field potentials from the hippocampus, reconstructed beamforming sources of scalp EEG, and – additionally in four participants – recorded from subdural cortical electrodes. When analyzing Granger causality, the information flow was from auditory cortex to hippocampus with a peak in the [4 8] Hz range while participants heard the letters. This flow was subsequently reversed during maintenance while participants maintained the letters in memory. The functional interaction between hippocampus and the cortex and the reversal of information flow provide a physiological basis for the encoding of memory items and their active replay during maintenance.