Publications

This paper describes a general model that subsumes many parametric models for continuous data. The model comprises hidden layers of state-space or dynamic causal models, arranged so that the output of one provides input to another. The ensuing hierarchy furnishes a model for many types of data, of arbitrary complexity. Special cases range from the general linear model for static data to generalised convolution models, with system noise, for nonlinear time-series analysis. Crucially, all of these models can be inverted using exactly the same scheme, namely, dynamic expectation maximization. This means that a single model and optimisation scheme can be used to invert a wide range of models. We present the model and a brief review of its inversion to disclose the relationships among, apparently, diverse generative models of empirical data. We then show that this inversion can be formulated as a simple neural network and may provide a useful metaphor for inference and learning in the brain.

This note describes a Bayesian model selection or optimization procedure for post hoc inferences about reduced versions of a full model. The scheme provides the evidence (marginal likelihood) for any reduced model as a function of the posterior density over the parameters of the full model. It rests upon specifying models through priors on their parameters, under the assumption that the likelihood remains the same for all models considered. This provides a quick and efficient scheme for scoring arbitrarily large numbers of models, after inverting a single (full) model. In turn, this enables the selection among discrete models that are distinguished by the presence or absence of free parameters, where free parameters are effectively removed from the model using very precise shrinkage priors. An alternative application of this post hoc model selection considers continuous model spaces, defined in terms of hyperparameters (sufficient statistics) of the prior density over model parameters. In this instance, the prior (model) can be optimized with respect to its evidence. The expressions for model evidence become remarkably simple under the Laplace (Gaussian) approximation to the posterior density. Special cases of this scheme include Savage-Dickey density ratio tests for reduced models and automatic relevance determination in model optimization. We illustrate the approach using general linear models and a more complicated nonlinear state-space model.

Abstract This chapter debates the use of functional regions of interest (fROI) and questions the validity of matching brains purely on the basis of structure in group analyses. It discusses an important misconception about factorial designs. The chapter addresses the structure–function relationship. Finally, it provides a conclusion and presents several appendices related to the topic.

Postulating that the brain performs approximate Bayesian inference generates principled and empirically testable models of neuronal function-the subject of much current interest in neuroscience and related disciplines. Current formulations address inference and learning under some assumed and particular model. In reality, organisms are often faced with an additional challenge-that of determining which model or models of their environment are the best for guiding behavior. Bayesian model averaging-which says that an agent should weight the predictions of different models according to their evidence-provides a principled way to solve this problem. Importantly, because model evidence is determined by both the accuracy and complexity of the model, optimal inference requires that these be traded off against one another. This means an agent's behavior should show an equivalent balance. We hypothesize that Bayesian model averaging plays an important role in cognition, given that it is both optimal and realizable within a plausible neuronal architecture. We outline model averaging and how it might be implemented, and then explore a number of implications for brain and behavior. In particular, we propose that model averaging can explain a number of apparently suboptimal phenomena within the framework of approximate (bounded) Bayesian inference, focusing particularly upon the relationship between goal-directed and habitual behavior.

Abstract To control our actions efficiently, our brain represents our body based on a combination of visual and proprioceptive cues, weighted according to how (un)reliable—how precise—each respective modality is in a given context. However, perceptual experiments in other modalities suggest that the weights assigned to sensory cues are also modulated “top-down” by attention. Here, we asked whether during action, attention can likewise modulate the weights (i.e., precision) assigned to visual versus proprioceptive information about body position. Participants controlled a virtual hand (VH) via a data glove, matching either the VH or their (unseen) real hand (RH) movements to a target, and thus adopting a ``visual'' or ``proprioceptive'' attentional set, under varying levels of visuo-proprioceptive congruence and visibility. Functional magnetic resonance imaging (fMRI) revealed increased activation of the multisensory superior parietal lobe (SPL) during the VH task and increased activation of the secondary somatosensory cortex (S2) during the RH task. Dynamic causal modeling (DCM) showed that these activity changes were the result of selective, diametrical gain modulations in the primary visual cortex (V1) and the S2. These results suggest that endogenous attention can balance the gain of visual versus proprioceptive brain areas, thus contextualizing their influence on multisensory areas representing the body for action.