Brandon M. Turner

A Bayesian framework for simultaneously modeling neural and behavioral data

Scientists who study cognition infer underlying processes either by observing behavior (e.g., response times, percentage correct) or by observing neural activity (e.g., the BOLD response). These two types of observations have traditionally supported two separate lines of study. The first is led by cognitive modelers, who rely on behavior alone to support their computational theories. The second is led by cognitive neuroimagers, who rely on statistical models to link patterns of neural activity to experimental manipulations, often without any attempt to make a direct connection to an explicit computational theory. Here we present a flexible Bayesian framework for combining neural and cognitive models. Joining neuroimaging and computational modeling in a single hierarchical framework allows the neural data to influence the parameters of the cognitive model and allows behavioral data, even in the absence of neural data, to constrain the neural model. Critically, our Bayesian approach can reveal interactions between behavioral and neural parameters, and hence between neural activity and cognitive mechanisms. We demonstrate the utility of our approach with applications to simulated fMRI data with a recognition model and to diffusion-weighted imaging data with a response time model of perceptual choice.

A method for efficiently sampling from distributions with correlated dimensions.

Bayesian estimation has played a pivotal role in the understanding of individual differences. However, for many models in psychology, Bayesian estimation of model parameters can be difficult. One reason for this difficulty is that conventional sampling algorithms, such as Markov chain Monte Carlo (MCMC), can be inefficient and impractical when little is known about the target distribution--particularly the target distributions covariance structure. In this article, we highlight some reasons for this inefficiency and advocate the use of a population MCMC algorithm, called differential evolution Markov chain Monte Carlo (DE-MCMC), as a means of efficient proposal generation. We demonstrate in a simulation study that the performance of the DE-MCMC algorithm is unaffected by the correlation of the target distribution, whereas conventional MCMC performs substantially worse as the correlation increases. We then show that the DE-MCMC algorithm can be used to efficiently fit a hierarchical version of the linear ballistic accumulator model to response time data, which has proven to be a difficult task when conventional MCMC is used.

When the brain takes a break: a model-based analysis of mind wandering

Mind wandering is an ubiquitous phenomenon in everyday life. In the cognitive neurosciences, mind wandering has been associated with several distinct neural processes, most notably increased activity in the default mode network (DMN), suppressed activity within the anti-correlated (task-positive) network (ACN), and changes in neuromodulation. By using an integrative multimodal approach combining machine-learning techniques with modeling of latent cognitive processes, we show that mind wandering in humans is characterized by inefficiencies in executive control (task-monitoring) processes. This failure is predicted by a single-trial signature of (co)activations in the DMN, ACN, and neuromodulation, and accompanied by a decreased rate of evidence accumulation and response thresholds in the cognitive model.

Informing Cognitive Abstractions Through Neuroimaging: The Neural Drift Diffusion Model

Trial-to-trial fluctuations in an observers state of mind have a direct influence on their behavior. However, characterizing an observers state of mind is difficult to do with behavioral data alone, particularly on a single-trial basis. In this article, we extend a recently developed hierarchical Bayesian framework for integrating neurophysiological information into cognitive models. In so doing, we develop a novel extension of the well-studied drift diffusion model (DDM) that uses single-trial brain activity patterns to inform the behavioral model parameters. We first show through simulation how the model outperforms the traditional DDM in a prediction task with sparse data. We then fit the model to experimental data consisting of a speed-accuracy manipulation on a random dot motion task. We use our cognitive modeling approach to show how prestimulus brain activity can be used to simultaneously predict response accuracy and response time. We use our model to provide an explanation for how activity in a brain region affects the dynamics of the underlying decision process through mechanisms assumed by the model. Finally, we show that our model performs better than the traditional DDM through a cross-validation test. By combining accuracy, response time, and the blood oxygen level-dependent response into a unified model, the link between cognitive abstraction and neuroimaging can be better understood.

A dynamic stimulus-driven model of signal detection

Signal detection theory forms the core of many current models of cognition, including memory, choice, and categorization. However, the classic signal detection model presumes the a priori existence of fixed stimulus representations--usually Gaussian distributions--even when the observer has no experience with the task. Furthermore, the classic signal detection model requires the observer to place a response criterion along the axis of stimulus strength, and without theoretical elaboration, this criterion is fixed and independent of the observers experience. We present a dynamic, adaptive model that addresses these 2 long-standing issues. Our model describes how the stimulus representation can develop from a rough subjective prior and thereby explains changes in signal detection performance over time. The model structure also provides a basis for the signal detection decision that does not require the placement of a criterion along the axis of stimulus strength. We present simulations of the model to examine its behavior and several experiments that provide data to test the model. We also fit the model to recognition memory data and discuss the role that feedback plays in establishing stimulus representations.

A generalized, likelihood-free method for posterior estimation

Recent advancements in Bayesian modeling have allowed for likelihood-free posterior estimation. Such estimation techniques are crucial to the understanding of simulation-based models, whose likelihood functions may be difficult or even impossible to derive. However, current approaches are limited by their dependence on sufficient statistics and/or tolerance thresholds. In this article, we provide a new approach that requires no summary statistics, error terms, or thresholds and is generalizable to all models in psychology that can be simulated. We use our algorithm to fit a variety of cognitive models with known likelihood functions to ensure the accuracy of our approach. We then apply our method to two real-world examples to illustrate the types of complex problems our method solves. In the first example, we fit an error-correcting criterion model of signal detection, whose criterion dynamically adjusts after every trial. We then fit two models of choice response time to experimental data: the linear ballistic accumulator model, which has a known likelihood, and the leaky competing accumulator model, whose likelihood is intractable. The estimated posterior distributions of the two models allow for direct parameter interpretation and model comparison by means of conventional Bayesian statistics—a feat that was not previously possible.

Why more is better: Simultaneous modeling of EEG, fMRI, and behavioral data☆

The need to test a growing number of theories in cognitive science has led to increased interest in inferential methods that integrate multiple data modalities. In this manuscript, we show how a method for integrating three data modalities within a single framework provides (1) more detailed descriptions of cognitive processes and (2) more accurate predictions of unobserved data than less integrative methods. Specifically, we show how combining either EEG and fMRI with a behavioral model can perform substantially better than a behavioral-data-only model in both generative and predictive modeling analyses. We then show how a trivariate model - a model including EEG, fMRI, and behavioral data - outperforms bivariate models in both generative and predictive modeling analyses. Together, these results suggest that within an appropriate modeling framework, more data can be used to better constrain cognitive theory, and to generate more accurate predictions for behavioral and neural data.

Intertemporal Choice as Discounted Value Accumulation

Two separate cognitive processes are involved in choosing between rewards available at different points in time. The first is temporal discounting, which consists of combining information about the size and delay of prospective rewards to represent subjective values. The second involves a comparison of available rewards to enable an eventual choice on the basis of these subjective values. While several mathematical models of temporal discounting have been developed, the reward selection process has been largely unexplored. To address this limitation, we evaluated the applicability of the Linear Ballistic Accumulator (LBA) model as a theory of the selection process in intertemporal choice. The LBA model formalizes the selection process as a sequential sampling algorithm in which information about different choice options is integrated until a decision criterion is reached. We compared several versions of the LBA model to demonstrate that choice outcomes and response times in intertemporal choice are well captured by the LBA process. The relationship between choice outcomes and response times that derives from the LBA model cannot be explained by temporal discounting alone. Moreover, the drift rates that drive evidence accumulation in the best-fitting LBA model are related to independently estimated subjective values derived from various temporal discounting models. These findings provide a quantitative framework for predicting dynamics of choice-related activity during the reward selection process in intertemporal choice and link intertemporal choice to other classes of decisions in which the LBA model has been applied.

Hierarchical approximate Bayesian computation.

Approximate Bayesian computation (ABC) is a powerful technique for estimating the posterior distribution of a model’s parameters. It is especially important when the model to be fit has no explicit likelihood function, which happens for computational (or simulation-based) models such as those that are popular in cognitive neuroscience and other areas in psychology. However, ABC is usually applied only to models with few parameters. Extending ABC to hierarchical models has been difficult because high-dimensional hierarchical models add computational complexity that conventional ABC cannot accommodate. In this paper, we summarize some current approaches for performing hierarchical ABC and introduce a new algorithm called Gibbs ABC. This new algorithm incorporates well-known Bayesian techniques to improve the accuracy and efficiency of the ABC approach for estimation of hierarchical models. We then use the Gibbs ABC algorithm to estimate the parameters of two models of signal detection, one with and one without a tractable likelihood function.

Likelihood-free Bayesian analysis of memory models.

Many influential memory models are computational in the sense that their predictions are derived through simulation. This means that it is difficult or impossible to write down a probability distribution or likelihood that characterizes the random behavior of the data as a function of the models parameters. In turn, the lack of a likelihood means that these models cannot be directly fitted to data using traditional techniques. In particular, standard Bayesian analyses of such models are impossible. In this article, we examine how a new procedure called approximate Bayesian computation (ABC), a method for Bayesian analysis that circumvents the evaluation of the likelihood, can be used to fit computational models to memory data. In particular, we investigate the bind cue decide model of episodic memory (Dennis & Humphreys, 2001) and the retrieving effectively from memory model (Shiffrin & Steyvers, 1997). We fit hierarchical versions of each model to the data of Dennis, Lee, and Kinnell (2008) and Kinnell and Dennis (2012). The ABC analysis permits us to explore the relationships between the parameters in each model as well as evaluate their relative fits to data-analyses that were not previously possible.