Optimizing Data for Modeling Neuronal Responses
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Plos Computational Biology 2018
RESEARCH ARTICLE Bayesian comparison of explicit and implicit causal inference strategies in multisensory heading perception Luigi Acerbi1☯¤*, Kalpana Dokka2☯, Dora E. Angelaki2, Wei Ji Ma1,3 1 Center for Neural Science, New York University, New York, NY, United States of America, 2 Department of Neuroscience, Baylor College of Medicine, Houston, TX, United States of America, 3 Department of Psychology, New York University, New York, NY, United States of America a1111111111 ☯ These authors contributed equally to this work. a1111111111 ¤ Current address: DeÂpartement des neurosciences fondamentales, Universite de Genève, Genève, a1111111111 Switzerland a1111111111 * [email protected], [email protected] a1111111111 Abstract The precision of multisensory perception improves when cues arising from the same cause OPEN ACCESS are integrated, such as visual and vestibular heading cues for an observer moving through a Citation: Acerbi L, Dokka K, Angelaki DE, Ma WJ stationary environment. In order to determine how the cues should be processed, the brain (2018) Bayesian comparison of explicit and implicit must infer the causal relationship underlying the multisensory cues. In heading perception, causal inference strategies in multisensory heading perception. PLoS Comput Biol 14(7): e1006110. however, it is unclear whether observers follow the Bayesian strategy, a simpler non-Bayes- https://doi.org/10.1371/journal.pcbi.1006110 ian heuristic, or even perform causal inference at all. We developed an efficient and robust Editor: Samuel J. Gershman, Harvard University, computational framework to perform Bayesian model comparison of causal inference strate- UNITED STATES gies, which incorporates a number of alternative assumptions about the observers. With this Received: July 26, 2017 framework, we investigated whether human observers' performance in an explicit cause attribution and an implicit heading discrimination task can be modeled as a causal inference Accepted: March 28, 2018 process. -
Bayesian Model Reduction
Bayesian model reduction Karl Friston, Thomas Parr and Peter Zeidman The Wellcome Centre for Human Neuroimaging, Institute of Neurology, University College London, UK. Correspondence: Peter Zeidman The Wellcome Centre for Human Neuroimaging Institute of Neurology 12 Queen Square, London, UK WC1N 3AR [email protected] Summary This paper reviews recent developments in statistical structure learning; namely, Bayesian model reduction. Bayesian model reduction is a method for rapidly computing the evidence and parameters of probabilistic models that differ only in their priors. In the setting of variational Bayes this has an analytical solution, which finesses the problem of scoring large model spaces in model comparison or structure learning. In this technical note, we review Bayesian model reduction and provide the relevant equations for several discrete and continuous probability distributions. We provide worked examples in the context of multivariate linear regression, Gaussian mixture models and dynamical systems (dynamic causal modelling). These examples are accompanied by the Matlab scripts necessary to reproduce the results. Finally, we briefly review recent applications in the fields of neuroimaging and neuroscience. Specifically, we consider structure learning and hierarchical or empirical Bayes that can be regarded as a metaphor for neurobiological processes like abductive reasoning. Keywords: Bayesian methods, empirical Bayes, model comparison, neurobiology, structure learning 1. Introduction Over the past years, Bayesian model comparison and structure learning have become key issues in the neurosciences (Collins and Frank, 2013, Friston et al., 2017a, Salakhutdinov et al., 2013, Tenenbaum et al., 2011, Tervo et al., 2016, Zorzi et al., 2013); particularly, in optimizing models of neuroimaging time series (Friston et al., 2015, Woolrich et al., 2009) and as a fundamental problem that our brains have to solve (Friston et al., 2017a, Schmidhuber, 1991, Schmidhuber, 2010). -
A Tutorial on Group Effective Connectivity Analysis, Part 2: Second Level Analysis with PEB
A tutorial on group effective connectivity analysis, part 2: second level analysis with PEB Peter Zeidman*1, Amirhossein Jafarian1, Mohamed L. Seghier2, Vladimir Litvak1, Hayriye Cagnan3, Cathy J. Price1, Karl J. Friston1 1 Wellcome Centre for Human Neuroimaging 12 Queen Square London WC1N 3AR 2 Cognitive Neuroimaging Unit, ECAE, Abu Dhabi, UAE 3 Nuffield Department of Clinical Neurosciences Level 6 West Wing John Radcliffe Hospital Oxford OX3 9DU * Corresponding author Conflicts of interest: None Abstract This tutorial provides a worked example of using Dynamic Causal Modelling (DCM) and Parametric Empirical Bayes (PEB) to characterise inter-subject variability in neural circuitry (effective connectivity). This involves specifying a hierarchical model with two or more levels. At the first level, state space models (DCMs) are used to infer the effective connectivity that best explains a subject’s neuroimaging timeseries (e.g. fMRI, MEG, EEG). Subject-specific connectivity parameters are then taken to the group level, where they are modelled using a General Linear Model (GLM) that partitions between-subject variability into designed effects and additive random effects. The ensuing (Bayesian) hierarchical model conveys both the estimated connection strengths and their uncertainty (i.e., posterior covariance) from the subject to the group level; enabling hypotheses to be tested about the commonalities and differences across subjects. This approach can also finesse parameter estimation at the subject level, by using the group-level parameters as empirical priors. We walk through this approach in detail, using data from a published fMRI experiment that characterised individual differences in hemispheric lateralization in a semantic processing task. The preliminary subject specific DCM analysis is covered in detail in a companion paper. -
Second Level Analysis with PEB
NeuroImage 200 (2019) 12–25 Contents lists available at ScienceDirect NeuroImage journal homepage: www.elsevier.com/locate/neuroimage A guide to group effective connectivity analysis, part 2: Second level analysis with PEB Peter Zeidman a,*, Amirhossein Jafarian a, Mohamed L. Seghier b, Vladimir Litvak a, Hayriye Cagnan c, Cathy J. Price a, Karl J. Friston a a Wellcome Centre for Human Neuroimaging, 12 Queen Square, London, WC1N 3AR, UK b Cognitive Neuroimaging Unit, ECAE, Abu Dhabi, United Arab Emirates c Nuffield Department of Clinical Neurosciences, Level 6, West Wing, John Radcliffe Hospital, Oxford, OX3 9DU, UK ABSTRACT This paper provides a worked example of using Dynamic Causal Modelling (DCM) and Parametric Empirical Bayes (PEB) to characterise inter-subject variability in neural circuitry (effective connectivity). It steps through an analysis in detail and provides a tutorial style explanation of the underlying theory and assumptions (i.e, priors). The analysis procedure involves specifying a hierarchical model with two or more levels. At the first level, state space models (DCMs) are used to infer the effective connectivity that best explains a subject's neuroimaging timeseries (e.g. fMRI, MEG, EEG). Subject-specific connectivity parameters are then taken to the group level, where they are modelled using a General Linear Model (GLM) that partitions between-subject variability into designed effects and additive random effects. The ensuing (Bayesian) hierarchical model conveys both the estimated connection strengths and their uncertainty (i.e., posterior covariance) from the subject to the group level; enabling hypotheses to be tested about the commonalities and differences across subjects. This approach can also finesse parameter estimation at the subject level, by using the group-level parameters as empirical priors.