Figure 7.

Estimation of coupling κ by four methods at different noise levels ζ. A range of κ from 0.5 to 3.5 was chosen based on the range of estimates observed in the analysis of experimental data. Decision noise levels were chosen in a range from very high (0.5) to very low (24). The remaining model parameters were held constant (ω = −4, ϑ = 0.0025). For each point of the resulting two-dimensional grid, 1000 task runs with 320 decisions each were simulated. Given the fixed sequence of inputs and simulated sequence of decisions, we then attempted to recover the model parameters, including κ and ζ, by four estimation methods: (1) the function Nelder-Mead simplex algorithm (NMSA), (2) Bayesian global optimization based on Gaussian processes (GPGO), (4) variational Bayes (VB), and Markov chain Monte Carlo sampling (MCMC). The figure shows boxplots of the distributions of the maximum-a-posteriori (MAP) point estimates for the four methods at each grid point. Boxplots consist of boxes spanning the range from the 25th to the 75th percentile, circles at the median, and whiskers spanning the rest of the estimate range. Horizontal shifts within ζ levels are for readability. Black bars indicate ground truth.