Dynamic causal modeling: Difference between revisions

Revision as of 15:34, 17 May 2018

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=== Neuroimaging ===

Bayesian model reduction was initially developed for use in neuroimaging analysis <ref name=":0" /><ref>{{Cite journal|last=Rosa|first=M.J.|last2=Friston|first2=K.|last3=Penny|first3=W.|date=2012-06|title=Post-hoc selection of dynamic causal models|url=https://doi.org/10.1016/j.jneumeth.2012.04.013|journal=Journal of Neuroscience Methods|volume=208|issue=1|pages=66–78|doi=10.1016/j.jneumeth.2012.04.013|issn=0165-0270|pmc=PMC3401996|pmid=22561579}}</ref>, in the context of modelling brain connectivity, as part of the [[Dynamic causal modelling]] framework (where it was originally referred to as post-hoc Bayesian model selection<ref name=":0" />). Dynamic causal models (DCMs) are differential equation models of brain dynamics, which<ref>{{Cite predictjournal|last=Friston|first=K.J.|last2=Harrison|first2=L.|last3=Penny|first3=W.|date=2003-08|title=Dynamic thecausal neuralmodelling|url=https://doi.org/10.1016/S1053-8119(03)00202-7|journal=NeuroImage|volume=19|issue=4|pages=1273–1302|doi=10.1016/s1053-8119(03)00202-7|issn=1053-8119}}</ref>. dynamicsThe andexperimenter neuroimagingspecifies timeseriesmultiple whichcompeting wouldmodels bewhich expecteddiffer givenin atheir particularpriors structure- ofi.e. neuralin connections.the Parametersset of theseparameters modelswhich are estimatedfixed usingat variationaltheir Bayesprior underexpectation theof Laplacezero. approximation,Having whichfitted meansa thatsingle the'full' priorsmodel andwith posteriorsall areparameters normallyof distributed.interest informed by the data, Bayesian model reduction enables the evidence (freeand energy)parameters for competing models to be rapidly computed, in order to test hypotheses. These models can be specified manually by the experimenter, or searched over automatically, in order to 'prune' any redundant parameters which do not contribute to the evidence.

ThisBayesian model approachreduction was subsequently generalised and applied to other forms of Bayesian models, for example hierarchical[[Empirical Bayes method|Parametric Empirical Bayes (PEB)]] models of group effects <ref name=":1" />. Here, it is used to compute the evidence and parameters for any given level of a hierarchical model under constraints (empirical priors) imposed from the level above.

=== Neurobiology ===

Bayesian model reduction has been used to explain functions of the brain, for instance where offline processing may eliminate redundant parameters of an internal world model. An example would be synaptic pruning in sleep <ref>{{Cite journal|last=Tononi|first=Giulio|last2=Cirelli|first2=Chiara|date=2006-02|title=Sleep function and synaptic homeostasis|url=https://doi.org/10.1016/j.smrv.2005.05.002|journal=Sleep Medicine Reviews|volume=10|issue=1|pages=49–62|doi=10.1016/j.smrv.2005.05.002|issn=1087-0792}}</ref>.

== Software implementations ==

Bayesian model reduction is implemented in the [[Statistical parametric mapping|Statistical Parametric Mapping]] toolbox, in the [[MATLAB|Matlab]] function [https://github.com/spm/spm12/blob/master/spm_log_evidence_reduce.m spm_log_evidence_reduce.m] .

== References ==