Fig 1.
The general structure of the BCI model and simulation results of BCI Toolbox.
(A) The generative model of BCI, assumes that there is either one cause (C = 1) or two causes (C = 2), leading to the creation of the perceptual variables (s or sA and sV). (B) The structure of the hierarchical BCI model in the BCI Toolbox. The causal structure is inferred by combining sensory likelihood and prior (prior stimulus expectation and pcommon. pcommon represents a priori expectation of a common cause). The observer response is based on the inferred causal structure, and the decision-making strategy. (C) The one-dimensional model simulation results (generated by pcommon = 0.5; σ1 = 3; σ2 = 8; σP = 30; μP = 0; s1 = -10; s2 = 10) from 3 different decision-making strategy using the BCI Toolbox.
Fig 2.
An overview of the BCI Toolbox GUI.
The GUI provides two main functions: model fitting and model simulation. In the model fitting section, the GUI incorporates two data types: discrete and continuous data. In the model simulation section, the GUI incorporates one-dimensional and two-dimensional simulations. For more details, see BCI Toolbox documentation: https://bcitoolboxrmd.readthedocs.io/.
Fig 3.
Results of parameter recovery analysis.
We generated 100 sets of synthetic data under 15 conditions by selecting random values for the 5 model parameters using the discrete 1-dimensional model simulation module of the toolbox. Next, the synthetic data were fitted by the data fitting module of the toolbox. In each panel, the estimated parameter value from data fitting is plotted against the ground-truth value of that parameter. R2 indicates the degree of correlation between the estimated and true parameters. MSE indicates the mean of squared error between data and identity lines (solid lines). In all cases, the model parameters were recovered well. (A) Results from using the Powell algorithm for parameter optimization. (B) Results from using the VBMC method for parameter optimization.
Fig 4.
Examples of BCI toolbox outputs.
(A) The model fitting results with continuous data from a spatial localization task. Each plot corresponds to one of the stimulus conditions, with the first row plots representing unisensory auditory conditions (stimulus position varying from left-most to right-most positions along azimuth from left to right), and first column representing unisensory visual conditions, and all other plots corresponding to bisensory conditions. Positions of the auditory and visual stimuli are denoted using broken red and blue vertical lines, respectively. The red and blue histograms represent the auditory and visual response distributions of a specific subject, respectively. The red and blue solid lines represent the model fits produced by the toolbox. (B) The simulation results for one visual stimulus accompanied by two auditory stimuli. We used the fixed parameters (Weak tendency: pcommon = 0.2; Strong tendency: pcommon = 0.8; σ1 = 1; σ2 = 0.5; σP = 1.5; μP = 1.5) to simulate how prior integration tendency influences multisensory numerosity perception. We also used the fixed parameters (pcommon = 0.5; Low visual precision: σ1 = 1; high visual precision: σ1 = 0.5; σ2 = 0.5; σP = 1.5; μP = 1.5) to simulate how unisensory precision influences multisensory numerosity perception.