Stochastic diffusion models ( Ratcliff, 1978 ) can be used to analyze response time data from binary decision tasks. They provide detailed information about cognitive processes underlying the performance in such tasks. Most importantly, different parameters are estimated from the response time distributions of correct responses and errors that map (1) the speed of information uptake, (2) the amount of information used to make a decision, (3) possible decision biases, and (4) the duration of nondecisional processes. Although this kind of model can be applied to many experimental paradigms and provides much more insight than the analysis of mean response times can, it is still rarely used in cognitive psychology. In the present paper, we provide comprehensive information on the theory of the diffusion model, as well as on practical issues that have to be considered for implementing the model.

Estimating the parameters of mathematical models is a common problem in almost all branches of science. However, this problem can prove notably difficult when processes and model descriptions become increasingly complex and an explicit likelihood function is not available. With this work, we propose a novel method for globally amortized Bayesian inference based on invertible neural networks that we call BayesFlow. The method uses simulations to learn a global estimator for the probabilistic mapping from observed data to underlying model parameters. A neural network pretrained in this way can then, without additional training or optimization, infer full posteriors on arbitrarily many real data sets involving the same model family. In addition, our method incorporates a summary network trained to embed the observed data into maximally informative summary statistics. Learning summary statistics from data makes the method applicable to modeling scenarios where standard inference techniques with handcrafted summary statistics fail. We demonstrate the utility of BayesFlow on challenging intractable models from population dynamics, epidemiology, cognitive science, and ecology. We argue that BayesFlow provides a general framework for building amortized Bayesian parameter estimation machines for any forward model from which data can be simulated.

Acting in accord with long-term goals requires control of interfering impulses, the success of which depends on several different processes. Using a structural-equation modeling approach, we investigated 5 behavioral components of impulsivity: the control of stimulus interference, proactive interference, and response interference, as well as decisional and motivational impulsivity. Results support the existence of 5 correlated but separable components of impulsive behavior. The present study is the 1st to demonstrate the separability of stimulus and response interference. It also supports the notion that control of response-related interference is not a unitary construct: Response-selection demands were separable from those of withholding or stopping. Relations between behavioral impulsivity components and self-report measures of impulsivity were largely absent. We conclude that as the construct of impulsivity has been extended to describe an increasingly diverse set of phenomena and processes, it has become too broad to be helpful in guiding future research.