Fig 1.
The simulation-based method of evaluating and optimizing experiment designs.
Note: light-blue elements denote required user inputs. (A) Dataset simulation process generates experiment realizations (e.g., cue-outcome sequences) and model responses (e.g., predicted physiological or behavioral responses), which together form a simulated dataset. (B) Dataset analysis applies the user-specified analysis procedure to the simulated dataset and produces analysis results (e.g., model evidence or parameter estimates). If the analysis procedure is Bayesian, an additional analysis prior needs to be specified. (C) The calculation of expected design utility requires simulating and analyzing a number of datasets. The user-defined utility function—which can depend directly on the design or on other simulation-specific quantities—provides the utility value for each simulated experiment. The expected design utility is obtained by averaging experiment-wise utilities. (D) Design optimization proceeds in iterations: the optimization algorithm proposes a design from the design space, the design is evaluated under the design prior, and the expected design utility is passed back to the optimizer. If the optimization satisfies the termination criterion (which is one of the user-defined optimization options), the optimizer returns the optimized design.
Fig 2.
Formalizing and parameterizing the structure of classical conditioning experiments.
(A) A conditioning trial can be represented as a Markov chain, parameterized by the probabilities of presenting different cues (e.g., colored shapes), and transition probabilities from cues to outcomes (e.g., delivery of shock vs. shock omission). (B) Stage-wise parameterization of conditioning experiments. Trials in each stage are generated by a Markov chain with constant transition probabilities. The transition probabilities of each stage are tunable design variables. (C) Periodic parameterization. The transition probabilities in the Markov chain are determined by square-periodic functions of time (i.e., trial number). The design variables are the two levels of the periodic function and its half-period.
Table 1.
Overview of user inputs for the three simulated scenarios.
Fig 3.
Design evaluation in Scenario 1: RW model learning rate estimation.
Three designs—reference acquisition-extinction design (REF), design optimized under a vague prior (VA-OPT), and design optimized under a point prior (PA-OPT)—are evaluated under the low (LA), middle (MA), and high (HA) value of the learning rate alpha. (A) Distribution of absolute errors in estimating the learning rate. (B) Pair-wise comparison of design accuracy expressed as the probability of the first design in the pair being superior (i.e., having lower estimation error). Error bars indicate bootstrapped 95% CI and 50% guideline indicates designs of equal quality. (C) Comparison of model responses (red full line) to the contingencies (black dashed line) obtained under different designs and different evaluation priors.
Fig 4.
Design evaluation in Scenario 2: Selection between RW and KRW models.
Three designs—reference backward blocking design (REF), design optimized under a vague prior (VP-OPT), and design optimized under a point prior (PP-OPT)—are evaluated under the ground truth model being either the RW or the KRW model. (A) Model selection accuracy (mean and the Clopper-Pearson binomial 95% CI). Horizontal guideline indicates chance level. Darker bars summarize results across ground truth models. (B) Values of the design variables in the two stages of the experiment: cue probabilities P(CS) and joint cue-outcome probabilities P(CS, US). (C) Comparison of fitted model responses obtained under different designs (rows) and different ground truth models (columns). Inset labels give the average difference in BIC (±SEM) between the fit of the true model and the alternative model (more negative values indicate stronger evidence in favor of the true model).
Fig 5.
Design evaluation in Scenario 3: Selection between RW and RWPH models.
Three designs—reference reversal learning design (REF), design optimized under a vague prior (VP-OPT), and design optimized under a point prior (PP-OPT)—are evaluated under the ground truth model being either the RW(V), RWPH(V), RWPH(α), or RWPH(V + α). (A) Model selection accuracy (mean and the Clopper-Pearson binomial 95% CI). Horizontal guideline indicates chance level. Darker bars summarize results across ground truth models. Inset shows the confusion matrix between the ground truth model (rows) and the selected model (columns). (B) Values of the design variables in the two stages of the experiment: cue probabilities P(CS) and joint cue-outcome probabilities P(CS, US). (C) Comparison of fitted RW(V) and RWPH(V + α) model responses obtained under different designs (rows) and these two models as assumed ground truth (columns). Inset labels give the average difference in BIC (±SEM) between the fit of the true model and the alternative model (more negative values indicate stronger evidence in favor of the true model). Note: the model responses are nearly identical when the RW(V) model is true, because this model is a special case of the alternative RWPH(V + α) model.