Comparing Families of Dynamic Causal Models
Publication Date
March 12, 2010
Journal
PLOS Computational Biology
Authors
Will D. Penny, Klaas E. Stephan, Jean Daunizeau, Maria J. Rosa, et al
Volume
6
Issue
3
Pages
e1000709
DOI
http://doi.org/10.1371/journal.pcbi.1000709
Publisher URL
http://journals.plos.org/ploscompbiol/article?id=10.1371%2Fjournal.pcbi.1000709
PubMed
http://www.ncbi.nlm.nih.gov/pubmed/20300649
PubMed Central
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC2837394
Europe PMC
http://europepmc.org/abstract/MED/20300649
Web of Science
000278125200017
Scopus
77950830678
Mendeley
http://www.mendeley.com/research/comparing-families-dynamic-causal-models
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Mendeley | Further Information

{"title"=>"Comparing families of dynamic causal models", "type"=>"journal", "authors"=>[{"first_name"=>"Will D.", "last_name"=>"Penny", "scopus_author_id"=>"7006713116"}, {"first_name"=>"Klaas E.", "last_name"=>"Stephan", "scopus_author_id"=>"7102375486"}, {"first_name"=>"Jean", "last_name"=>"Daunizeau", "scopus_author_id"=>"21742214400"}, {"first_name"=>"Maria J.", "last_name"=>"Rosa", "scopus_author_id"=>"34882137100"}, {"first_name"=>"Karl J.", "last_name"=>"Friston", "scopus_author_id"=>"36080215500"}, {"first_name"=>"Thomas M.", "last_name"=>"Schofield", "scopus_author_id"=>"24466698800"}, {"first_name"=>"Alex P.", "last_name"=>"Leff", "scopus_author_id"=>"7102799047"}], "year"=>2010, "source"=>"PLoS Computational Biology", "identifiers"=>{"isbn"=>"1553-7358 (Electronic)\\r1553-734X (Linking)", "doi"=>"10.1371/journal.pcbi.1000709", "pui"=>"358620662", "sgr"=>"77950830678", "scopus"=>"2-s2.0-77950830678", "pmid"=>"20300649", "issn"=>"1553734X"}, "id"=>"8c6406f5-0aa5-3e4c-9b4f-13086cee481f", "abstract"=>"Mathematical models of scientific data can be formally compared using Bayesian model evidence. Previous applications in the biological sciences have mainly focussed on model selection in which one first selects the model with the highest evidence and then makes inferences based on the parameters of that model. This \"best model\" approach is very useful but can become brittle if there are a large number of models to compare, and if different subjects use different models. To overcome this shortcoming we propose the combination of two further approaches: (i) family level inference and (ii) Bayesian model averaging within families. Family level inference removes uncertainty about aspects of model structure other than the characteristic of interest. For example: What are the inputs to the system? Is processing serial or parallel? Is it linear or nonlinear? Is it mediated by a single, crucial connection? We apply Bayesian model averaging within families to provide inferences about parameters that are independent of further assumptions about model structure. We illustrate the methods using Dynamic Causal Models of brain imaging data.", "link"=>"http://www.mendeley.com/research/comparing-families-dynamic-causal-models", "reader_count"=>399, "reader_count_by_academic_status"=>{"Unspecified"=>3, "Professor > Associate Professor"=>25, "Researcher"=>107, "Student > Doctoral Student"=>15, "Student > Ph. D. Student"=>145, "Student > Postgraduate"=>12, "Student > Master"=>42, "Other"=>5, "Student > Bachelor"=>21, "Lecturer"=>5, "Lecturer > Senior Lecturer"=>2, "Professor"=>17}, "reader_count_by_user_role"=>{"Unspecified"=>3, "Professor > Associate Professor"=>25, "Researcher"=>107, "Student > Doctoral Student"=>15, "Student > Ph. D. Student"=>145, "Student > Postgraduate"=>12, "Student > Master"=>42, "Other"=>5, "Student > Bachelor"=>21, "Lecturer"=>5, "Lecturer > Senior Lecturer"=>2, "Professor"=>17}, "reader_count_by_subject_area"=>{"Unspecified"=>30, "Agricultural and Biological Sciences"=>71, "Philosophy"=>3, "Business, Management and Accounting"=>1, "Computer Science"=>30, "Engineering"=>40, "Environmental Science"=>2, "Mathematics"=>10, "Medicine and Dentistry"=>54, "Neuroscience"=>49, "Physics and Astronomy"=>12, "Psychology"=>96, "Social Sciences"=>1}, "reader_count_by_subdiscipline"=>{"Medicine and Dentistry"=>{"Medicine and Dentistry"=>54}, "Social Sciences"=>{"Social Sciences"=>1}, "Physics and Astronomy"=>{"Physics and Astronomy"=>12}, "Psychology"=>{"Psychology"=>96}, "Mathematics"=>{"Mathematics"=>10}, "Unspecified"=>{"Unspecified"=>30}, "Environmental Science"=>{"Environmental Science"=>2}, "Engineering"=>{"Engineering"=>40}, "Neuroscience"=>{"Neuroscience"=>49}, "Agricultural and Biological Sciences"=>{"Agricultural and Biological Sciences"=>71}, "Computer Science"=>{"Computer Science"=>30}, "Business, Management and Accounting"=>{"Business, Management and Accounting"=>1}, "Philosophy"=>{"Philosophy"=>3}}, "reader_count_by_country"=>{"Colombia"=>1, "Hungary"=>1, "United States"=>10, "Japan"=>2, "United Kingdom"=>16, "Ghana"=>1, "Switzerland"=>4, "India"=>1, "Canada"=>2, "Austria"=>2, "Netherlands"=>1, "Turkey"=>1, "Iran"=>1, "Belgium"=>1, "Finland"=>1, "Italy"=>3, "France"=>6, "Australia"=>2, "Chile"=>1, "Germany"=>14}, "group_count"=>20}

CrossRef

Scopus | Further Information

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Figshare

  • {"files"=>["https://ndownloader.figshare.com/files/858349"], "description"=>"<p>The histograms show versus for the input families. Input family ‘P’ has the highest posterior expected probability . See <a href=\"http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1000709#pcbi-1000709-t001\" target=\"_blank\">Table 1</a> for other posterior expectations.</p>", "links"=>[], "tags"=>["posterior", "densities"], "article_id"=>528801, "categories"=>["Computational Biology", "Mathematics", "Neuroscience", "Medicine"], "users"=>["Will D. Penny", "Klaas E. Stephan", "Jean Daunizeau", "Maria J. Rosa", "Karl J. Friston", "Thomas M. Schofield", "Alex P. Leff"], "doi"=>"https://dx.doi.org/10.1371/journal.pcbi.1000709.g002", "stats"=>{"downloads"=>1, "page_views"=>6, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_RFX_posterior_densities_for_input_families_/528801", "title"=>"RFX posterior densities for input families.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2010-03-12 02:26:41"}
  • {"files"=>["https://ndownloader.figshare.com/files/858935"], "description"=>"<p>The figures show the posterior densities of average network parameters from random effects Bayesian model averaging for the modulatory connections. Only forward connections from P to A and from P to F are modulated by speech intelligibility.</p>", "links"=>[], "tags"=>["modulatory", "connections", "rfx"], "article_id"=>529381, "categories"=>["Computational Biology", "Mathematics", "Neuroscience", "Medicine"], "users"=>["Will D. Penny", "Klaas E. Stephan", "Jean Daunizeau", "Maria J. Rosa", "Karl J. Friston", "Thomas M. Schofield", "Alex P. Leff"], "doi"=>"https://dx.doi.org/10.1371/journal.pcbi.1000709.g008", "stats"=>{"downloads"=>1, "page_views"=>5, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Average_Modulatory_Connections_from_RFX_for_input_family_P_/529381", "title"=>"Average Modulatory Connections from RFX for input family P.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2010-03-12 02:36:21"}
  • {"files"=>["https://ndownloader.figshare.com/files/858644"], "description"=>"<p>For FFX (top panel) the figure shows that models in the F and BAL families have most probability mass. The expected posteriors from the RFX inference show a similar pattern (bottom panel). The ordering of models in this figure is not the same as the ordering of P models in <a href=\"http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1000709#pcbi-1000709-g004\" target=\"_blank\">figure 4</a>.</p>", "links"=>[], "tags"=>["inference", "modulatory"], "article_id"=>529094, "categories"=>["Computational Biology", "Mathematics", "Neuroscience", "Medicine"], "users"=>["Will D. Penny", "Klaas E. Stephan", "Jean Daunizeau", "Maria J. Rosa", "Karl J. Friston", "Thomas M. Schofield", "Alex P. Leff"], "doi"=>"https://dx.doi.org/10.1371/journal.pcbi.1000709.g005", "stats"=>{"downloads"=>0, "page_views"=>4, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Model_level_inference_for_modulatory_families_/529094", "title"=>"Model level inference for modulatory families.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2010-03-12 02:31:34"}
  • {"files"=>["https://ndownloader.figshare.com/files/859028"], "description"=>"<p>All values are tabulated to two decimal places (dp). For an FFX inference, the alternative probability for input family is . The expected and exceedance probabilities for RFX were computed from the posterior densities shown in <a href=\"http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1000709#pcbi-1000709-g002\" target=\"_blank\">Figure 2</a>. For RFX inference the total exceedance probability that either region A alone or region P alone receives auditory input is .</p>", "links"=>[], "tags"=>["computational biology/computational neuroscience", "computational biology/metabolic networks", "computational biology/systems biology", "computational biology/transcriptional regulation", "mathematics/statistics", "neuroscience/cognitive neuroscience", "neuroscience/theoretical neuroscience"], "article_id"=>529479, "categories"=>["Computational Biology", "Mathematics", "Neuroscience", "Medicine"], "users"=>["Will D. Penny", "Klaas E. Stephan", "Jean Daunizeau", "Maria J. Rosa", "Karl J. Friston", "Thomas M. Schofield", "Alex P. Leff"], "doi"=>"https://dx.doi.org/10.1371/journal.pcbi.1000709.t001", "stats"=>{"downloads"=>6, "page_views"=>2, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Inference_over_input_families_/529479", "title"=>"Inference over input families.", "pos_in_sequence"=>0, "defined_type"=>3, "published_date"=>"2010-03-12 02:37:59"}
  • {"files"=>["https://ndownloader.figshare.com/files/858745"], "description"=>"<p>The figure shows the input (filled square and solid arrow) and modulatory connectivity (solid arrows) stuctures for four models in Occam's window (assessed using FFX). Note that all models also have full endogenous connectivity (not shown). These four models are (a) model with , rank = 1, (b) model with , rank = 2, (c) model with , rank = 15 and (d) model with , rank = 16. All models have auditory input entering region P.</p>", "links"=>[], "tags"=>["computational biology/computational neuroscience", "computational biology/metabolic networks", "computational biology/systems biology", "computational biology/transcriptional regulation", "mathematics/statistics", "neuroscience/cognitive neuroscience", "neuroscience/theoretical neuroscience"], "article_id"=>529194, "categories"=>["Computational Biology", "Mathematics", "Neuroscience", "Medicine"], "users"=>["Will D. Penny", "Klaas E. Stephan", "Jean Daunizeau", "Maria J. Rosa", "Karl J. Friston", "Thomas M. Schofield", "Alex P. Leff"], "doi"=>"https://dx.doi.org/10.1371/journal.pcbi.1000709.g006", "stats"=>{"downloads"=>4, "page_views"=>11, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Likely_models_/529194", "title"=>"Likely models.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2010-03-12 02:33:14"}
  • {"files"=>["https://ndownloader.figshare.com/files/859068"], "description"=>"<p>All values are tabulated to two decimal places (dp).</p>", "links"=>[], "tags"=>["modulatory"], "article_id"=>529522, "categories"=>["Computational Biology", "Mathematics", "Neuroscience", "Medicine"], "users"=>["Will D. Penny", "Klaas E. Stephan", "Jean Daunizeau", "Maria J. Rosa", "Karl J. Friston", "Thomas M. Schofield", "Alex P. Leff"], "doi"=>"https://dx.doi.org/10.1371/journal.pcbi.1000709.t002", "stats"=>{"downloads"=>1, "page_views"=>5, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Inference_over_modulatory_families_/529522", "title"=>"Inference over modulatory families.", "pos_in_sequence"=>0, "defined_type"=>3, "published_date"=>"2010-03-12 02:38:42"}
  • {"files"=>["https://ndownloader.figshare.com/files/858822"], "description"=>"<p>The figures show the posterior densities of average network parameters from fixed effects Bayesian model averaging for the modulatory connections. Only forward connections from P to A and from P to F are modulated by speech intelligibility.</p>", "links"=>[], "tags"=>["modulatory", "connections", "ffx"], "article_id"=>529270, "categories"=>["Computational Biology", "Mathematics", "Neuroscience", "Medicine"], "users"=>["Will D. Penny", "Klaas E. Stephan", "Jean Daunizeau", "Maria J. Rosa", "Karl J. Friston", "Thomas M. Schofield", "Alex P. Leff"], "doi"=>"https://dx.doi.org/10.1371/journal.pcbi.1000709.g007", "stats"=>{"downloads"=>1, "page_views"=>6, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Average_Modulatory_Connections_from_FFX_for_input_family_P_/529270", "title"=>"Average Modulatory Connections from FFX for input family P.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2010-03-12 02:34:30"}
  • {"files"=>["https://ndownloader.figshare.com/files/426787"], "description"=>"<div><p>Mathematical models of scientific data can be formally compared using Bayesian model evidence. Previous applications in the biological sciences have mainly focussed on model selection in which one first selects the model with the highest evidence and then makes inferences based on the parameters of that model. This “best model” approach is very useful but can become brittle if there are a large number of models to compare, and if different subjects use different models. To overcome this shortcoming we propose the combination of two further approaches: (i) family level inference and (ii) Bayesian model averaging within families. Family level inference removes uncertainty about aspects of model structure other than the characteristic of interest. For example: What are the inputs to the system? Is processing serial or parallel? Is it linear or nonlinear? Is it mediated by a single, crucial connection? We apply Bayesian model averaging within families to provide inferences about parameters that are independent of further assumptions about model structure. We illustrate the methods using Dynamic Causal Models of brain imaging data.</p></div>", "links"=>[], "tags"=>["comparing", "causal", "models"], "article_id"=>144248, "categories"=>["Biological Sciences", "Mathematics", "Neuroscience", "Medicine"], "users"=>["Will D. Penny", "Klaas E. Stephan", "Jean Daunizeau", "Maria J. Rosa", "Karl J. Friston", "Thomas M. Schofield", "Alex P. Leff"], "doi"=>"https://dx.doi.org/10.1371/journal.pcbi.1000709", "stats"=>{"downloads"=>21, "page_views"=>6, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/Comparing_Families_of_Dynamic_Causal_Models/144248", "title"=>"Comparing Families of Dynamic Causal Models", "pos_in_sequence"=>0, "defined_type"=>3, "published_date"=>"2010-03-12 01:10:48"}
  • {"files"=>["https://ndownloader.figshare.com/files/858397"], "description"=>"<p>The histograms show versus for the modulatory families. Modulatory family ‘F’ has the highest posterior expected probability . See <a href=\"http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1000709#pcbi-1000709-t002\" target=\"_blank\">Table 2</a> for other posterior expectations.</p>", "links"=>[], "tags"=>["posterior", "densities", "modulatory"], "article_id"=>528857, "categories"=>["Computational Biology", "Mathematics", "Neuroscience", "Medicine"], "users"=>["Will D. Penny", "Klaas E. Stephan", "Jean Daunizeau", "Maria J. Rosa", "Karl J. Friston", "Thomas M. Schofield", "Alex P. Leff"], "doi"=>"https://dx.doi.org/10.1371/journal.pcbi.1000709.g003", "stats"=>{"downloads"=>1, "page_views"=>4, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_RFX_Posterior_densities_for_modulatory_families_/528857", "title"=>"RFX Posterior densities for modulatory families.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2010-03-12 02:27:37"}
  • {"files"=>["https://ndownloader.figshare.com/files/858276"], "description"=>"<p>The DCMs in this paper were used to analyse fMRI data from three brain regions: (i) left posterior temporal sulcus (region P), (ii) left anterior superior temporal sulcus (region A) and (iii) pars orbitalis of the inferior frontal gyrus (region F). The DCMs themselves comprised the following variables; experimental inputs for auditory stimulation and for speech intelligibility, a neuronal activity vector with three elements (one for each region P, A, and F), exogenous connections specified by the three-by-three connectivity matrix (dotted arrows in figure), modulatory connections specified by three-by-three modulatory matrics for inputs (the solid line ending with a filled circle denotes the single non-zero entry for this particular model), and a 3-by-2 direct input connectivity matrix with non-zero entries shown by solid arrows. The dynamics of this model are govenered by equation 1. All DCMs in this paper used all-to-all endogenous connectivity ie. there were endogenous connections between all three regions. Different models were set up by specifying which regions received direct (auditory) input (non-zero entries in ) and which connections could be modulated by the speech intelligibility (non-zero entries in the matrix ).</p>", "links"=>[], "tags"=>["causal"], "article_id"=>528731, "categories"=>["Computational Biology", "Mathematics", "Neuroscience", "Medicine"], "users"=>["Will D. Penny", "Klaas E. Stephan", "Jean Daunizeau", "Maria J. Rosa", "Karl J. Friston", "Thomas M. Schofield", "Alex P. Leff"], "doi"=>"https://dx.doi.org/10.1371/journal.pcbi.1000709.g001", "stats"=>{"downloads"=>2, "page_views"=>6, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Dynamic_Causal_Models_/528731", "title"=>"Dynamic Causal Models.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2010-03-12 02:25:31"}
  • {"files"=>["https://ndownloader.figshare.com/files/858529"], "description"=>"<p>For FFX (top panel) the figure shows that models in the P family have by far the greatest posterior probability mass. For RFX (bottom panel) models in both A and P families have high posterior expected probability, although the probability mass for P dominates.</p>", "links"=>[], "tags"=>["inference"], "article_id"=>528989, "categories"=>["Computational Biology", "Mathematics", "Neuroscience", "Medicine"], "users"=>["Will D. Penny", "Klaas E. Stephan", "Jean Daunizeau", "Maria J. Rosa", "Karl J. Friston", "Thomas M. Schofield", "Alex P. Leff"], "doi"=>"https://dx.doi.org/10.1371/journal.pcbi.1000709.g004", "stats"=>{"downloads"=>1, "page_views"=>2, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Model_level_inference_for_input_families_/528989", "title"=>"Model level inference for input families.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2010-03-12 02:29:49"}

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Relative Metric

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