Analysing brain networks in population neuroscience: a case for the Bayesian philosophy

Network connectivity fingerprints are among today's best choices to obtain a faithful sampling of an individual's brain and cognition. Widely available MRI scanners can provide rich information tapping into network recruitment and reconfiguration that now scales to hundreds and thousands of humans. Here, we contemplate the advantages of analysing such connectome profiles using Bayesian strategies. These analysis techniques afford full probability estimates of the studied network coupling phenomena, provide analytical machinery to separate epistemological uncertainty and biological variability in a coherent manner, usher us towards avenues to go beyond binary statements on existence versus non-existence of an effect, and afford credibility estimates around all model parameters at play which thus enable single-subject predictions with rigorous uncertainty intervals. We illustrate the brittle boundary between healthy and diseased brain circuits by autism spectrum disorder as a recurring theme where, we argue, network-based approaches in neuroscience will require careful probabilistic answers. This article is part of the theme issue ‘Unifying the essential concepts of biological networks: biological insights and philosophical foundations’.

[1]  Thomas V. Wiecki,et al.  10,000 social brains: Sex differentiation in human brain anatomy , 2020, Science Advances.

[2]  Radford M. Neal Pattern Recognition and Machine Learning , 2007, Technometrics.

[3]  B. T. Thomas Yeo,et al.  Inference in the age of big data: Future perspectives on neuroscience , 2017, NeuroImage.

[4]  Stephen J. Roberts,et al.  A tutorial on variational Bayesian inference , 2012, Artificial Intelligence Review.

[5]  A. Nobel,et al.  Statistical Significance of Clustering for High-Dimension, Low–Sample Size Data , 2008 .

[6]  Connie Kasari,et al.  The art of camouflage: Gender differences in the social behaviors of girls and boys with autism spectrum disorder , 2017, Autism : the international journal of research and practice.

[7]  Ole Winther,et al.  Bayesian Non-negative Matrix Factorization , 2009, ICA.

[8]  Lou Massa,et al.  Notes on The Energy Equivalence of Information. , 2017, The journal of physical chemistry. A.

[9]  D. Geschwind,et al.  Autism spectrum disorders: developmental disconnection syndromes , 2007, Current Opinion in Neurobiology.

[10]  Hyun-Han Kwon,et al.  A Bayesian beta distribution model for estimating rainfall IDF curves in a changing climate , 2016 .

[11]  Shai Ben-David,et al.  Understanding Machine Learning: From Theory to Algorithms , 2014 .

[12]  G. A. Miller,et al.  Misunderstanding analysis of covariance. , 2001, Journal of abnormal psychology.

[13]  Adriana Di Martino,et al.  Reconciling Dimensional and Categorical Models of Autism Heterogeneity: A Brain Connectomics and Behavioral Study , 2019, Biological Psychiatry.

[14]  École d'été de probabilités de Saint-Flour,et al.  École d'été de probabilités de Saint-Flour XIII - 1983 , 1985 .

[15]  Rafael Malach,et al.  Disrupted Neural Synchronization in Toddlers with Autism , 2011, Neuron.

[16]  Karl J. Friston,et al.  Computational neuroimaging strategies for single patient predictions , 2017, NeuroImage.

[17]  Dhruman Goradia,et al.  Corpus Callosum Volume and Neurocognition in Autism , 2009, Journal of autism and developmental disorders.

[18]  Carl E. Rasmussen,et al.  The Infinite Gaussian Mixture Model , 1999, NIPS.

[19]  Anil K. Ghosh,et al.  On some graph-based two-sample tests for high dimension, low sample size data , 2019, Machine Learning.

[20]  M. Chun,et al.  Functional connectome fingerprinting: Identifying individuals based on patterns of brain connectivity , 2015, Nature Neuroscience.

[21]  I. Mazin,et al.  Theory , 1934 .

[22]  A. Meyer-Lindenberg,et al.  Machine Learning for Precision Psychiatry: Opportunities and Challenges. , 2017, Biological psychiatry. Cognitive neuroscience and neuroimaging.

[23]  Mark W. Woolrich,et al.  Multilevel linear modelling for FMRI group analysis using Bayesian inference , 2004, NeuroImage.

[24]  Matthew J. Beal Variational algorithms for approximate Bayesian inference , 2003 .

[25]  In Kyoon Lyoo,et al.  Laterobasal amygdalar enlargement in 6- to 7-year-old children with autism spectrum disorder. , 2010, Archives of general psychiatry.

[26]  B. Efron Bootstrap Methods: Another Look at the Jackknife , 1979 .

[27]  Karl J. Friston,et al.  Dynamic causal modelling , 2003, NeuroImage.

[28]  Nancy Kanwisher,et al.  Spurious group differences due to head motion in a diffusion MRI study , 2013, NeuroImage.

[29]  Mark W. Woolrich,et al.  Bayesian inference in FMRI , 2012, NeuroImage.

[30]  Michael V. Lombardo,et al.  Sex/Gender Differences and Autism: Setting the Scene for Future Research , 2015, Journal of the American Academy of Child and Adolescent Psychiatry.

[31]  Karl J. Friston,et al.  Classical and Bayesian Inference in Neuroimaging: Applications , 2002, NeuroImage.

[32]  Adeel Razi,et al.  A DCM for resting state fMRI , 2014, NeuroImage.

[33]  L. Kanner Autistic disturbances of affective contact. , 1968, Acta paedopsychiatrica.

[34]  Daniel P. Kennedy,et al.  The Autism Brain Imaging Data Exchange: Towards Large-Scale Evaluation of the Intrinsic Brain Architecture in Autism , 2013, Molecular Psychiatry.

[35]  J. Kruschke Doing Bayesian Data Analysis , 2010 .

[36]  Paula Smith,et al.  “Putting on My Best Normal”: Social Camouflaging in Adults with Autism Spectrum Conditions , 2017, Journal of Autism and Developmental Disorders.

[37]  Charles Kemp,et al.  How to Grow a Mind: Statistics, Structure, and Abstraction , 2011, Science.

[38]  Vincent Frouin,et al.  Dissecting the heterogeneous cortical anatomy of autism spectrum disorder using normative models , 2018 .

[39]  S. Baron-Cohen,et al.  Imaging sex/gender and autism in the brain: Etiological implications , 2017, Journal of neuroscience research.

[40]  S. Blakemore,et al.  Studying individual differences in human adolescent brain development , 2018, Nature Neuroscience.

[41]  Karl J. Friston,et al.  Posterior probability maps and SPMs , 2003, NeuroImage.

[42]  D. Pfaff,et al.  Etiologies underlying sex differences in Autism Spectrum Disorders , 2014, Frontiers in Neuroendocrinology.

[43]  E. Bullmore,et al.  The amygdala theory of autism , 2000, Neuroscience & Biobehavioral Reviews.

[44]  N. Volkow,et al.  The conception of the ABCD study: From substance use to a broad NIH collaboration , 2017, Developmental Cognitive Neuroscience.

[45]  Torrin M. Liddell,et al.  The Bayesian New Statistics: Hypothesis testing, estimation, meta-analysis, and power analysis from a Bayesian perspective , 2016, Psychonomic bulletin & review.

[46]  Hedvig Kjellström,et al.  Advances in Variational Inference , 2017, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[47]  H. Jeffreys An invariant form for the prior probability in estimation problems , 1946, Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences.

[48]  Michael P. Milham,et al.  Network-specific sex differentiation of intrinsic brain function in males with autism , 2018, Molecular Autism.

[49]  Adeel Razi,et al.  Bayesian model reduction and empirical Bayes for group (DCM) studies , 2016, NeuroImage.

[50]  Jonathan D. Power,et al.  Prediction of Individual Brain Maturity Using fMRI , 2010, Science.

[51]  Christine Wu Nordahl,et al.  Brief Report: Methods for Acquiring Structural MRI Data in Very Young Children with Autism Without the Use of Sedation , 2008, Journal of autism and developmental disorders.

[52]  Lisa Byrge,et al.  Nonreplication of functional connectivity differences in autism spectrum disorder across multiple sites and denoising strategies , 2019, bioRxiv.

[53]  David J. C. MacKay,et al.  Information Theory, Inference, and Learning Algorithms , 2004, IEEE Transactions on Information Theory.

[54]  C. Beckmann,et al.  Beyond Lumping and Splitting: A Review of Computational Approaches for Stratifying Psychiatric Disorders , 2016, Biological psychiatry. Cognitive neuroscience and neuroimaging.

[55]  Tom Johnstone,et al.  Amygdala Volume and Nonverbal Social Impairment in Adolescent and Adult Males with Autism , 2022 .

[56]  Daniel Rueckert,et al.  A spatio-temporal reference model of the aging brain , 2018, NeuroImage.

[57]  Alex Kendall,et al.  What Uncertainties Do We Need in Bayesian Deep Learning for Computer Vision? , 2017, NIPS.

[58]  Marcel van Gerven,et al.  Probabilistic model-based functional parcellation reveals a robust, fine-grained subdivision of the striatum , 2015, NeuroImage.

[59]  B. H. Lo,et al.  Autism Spectrum Disorder , 2018, Journal of paediatrics and child health.

[60]  Fernando Pérez-Cruz,et al.  Bayesian nonparametric comorbidity analysis of psychiatric disorders , 2014, J. Mach. Learn. Res..

[61]  B. B. Meshram,et al.  Modeling Rainfall Prediction Using Data Mining Method: A Bayesian Approach , 2013, 2013 Fifth International Conference on Computational Intelligence, Modelling and Simulation.

[62]  T. Bayes An essay towards solving a problem in the doctrine of chances , 2003 .

[63]  Andre F. Marquand,et al.  From pattern classification to stratification: towards conceptualizing the heterogeneity of Autism Spectrum Disorder , 2019, Neuroscience & Biobehavioral Reviews.

[64]  Richard F. Betzel,et al.  Linked dimensions of psychopathology and connectivity in functional brain networks , 2017, bioRxiv.

[65]  David Hinkley,et al.  Bootstrap Methods: Another Look at the Jackknife , 2008 .

[66]  Thomas L. Griffiths,et al.  The Indian Buffet Process: An Introduction and Review , 2011, J. Mach. Learn. Res..

[67]  G. Varoquaux,et al.  Connectivity‐based parcellation: Critique and implications , 2015, Human brain mapping.

[68]  D. Cox FREQUENTIST AND BAYESIAN STATISTICS: A CRITIQUE , 2006 .

[69]  Karl J. Friston,et al.  Classical and Bayesian Inference in Neuroimaging: Theory , 2002, NeuroImage.

[70]  Zoubin Ghahramani,et al.  Probabilistic machine learning and artificial intelligence , 2015, Nature.

[71]  Luca Ambrogioni,et al.  Structurally-informed Bayesian functional connectivity analysis , 2014, NeuroImage.

[72]  Vince D. Calhoun,et al.  Single subject prediction of brain disorders in neuroimaging: Promises and pitfalls , 2017, NeuroImage.

[73]  D. Aldous Exchangeability and related topics , 1985 .

[74]  Thomas E. Nichols,et al.  A positive-negative mode of population covariation links brain connectivity, demographics and behavior , 2015, Nature Neuroscience.

[75]  M. Chun,et al.  A neuromarker of sustained attention from whole-brain functional connectivity , 2015, Nature Neuroscience.

[76]  André Zugman,et al.  Commentary: Functional connectome fingerprint: identifying individuals using patterns of brain connectivity , 2017, Front. Hum. Neurosci..

[77]  Tom Lodewyckx,et al.  Bayesian Versus Frequentist Inference , 2008 .

[78]  Mark W. Woolrich,et al.  Bayesian analysis of neuroimaging data in FSL , 2009, NeuroImage.

[79]  Jon M. Kleinberg,et al.  An Impossibility Theorem for Clustering , 2002, NIPS.

[80]  A brief summary of the articles appearing in this issue of Biological Psychiatry: Cognitive Neuroscience and Neuroimaging. , 2017, Biological psychiatry. Cognitive neuroscience and neuroimaging.

[81]  Karl J. Friston,et al.  Variational free energy and the Laplace approximation , 2007, NeuroImage.

[82]  Abraham Z. Snyder,et al.  Spurious but systematic correlations in functional connectivity MRI networks arise from subject motion , 2012, NeuroImage.

[83]  John K Kruschke,et al.  Bayesian data analysis. , 2010, Wiley interdisciplinary reviews. Cognitive science.

[84]  Mélanie Frappier,et al.  The Book of Why: The New Science of Cause and Effect , 2018, Science.

[85]  A. Richardson,et al.  A Critique of , 2009 .

[86]  Danilo Bzdok,et al.  Classical Statistics and Statistical Learning in Imaging Neuroscience , 2016, Front. Neurosci..

[87]  Michael C. Frank,et al.  Estimating the reproducibility of psychological science , 2015, Science.

[88]  Naomi Oreskes,et al.  Assessing climate change impacts on extreme weather events: the case for an alternative (Bayesian) approach , 2017, Climatic Change.

[89]  Carl E. Rasmussen,et al.  Gaussian processes for machine learning , 2005, Adaptive computation and machine learning.

[90]  A. McIntosh,et al.  Functional connectivity-based subtypes of individuals with and without autism spectrum disorder , 2019, Network Neuroscience.

[91]  S. F.R.,et al.  An Essay towards solving a Problem in the Doctrine of Chances . By the late Rev . Mr . Bayes , communicated by Mr . Price , in a letter to , 1999 .

[92]  Thomas E. Nichols,et al.  Towards algorithmic analytics for large-scale datasets , 2019, Nature Machine Intelligence.

[93]  Lisa Byrge,et al.  Non-replication of functional connectivity differences in autism spectrum disorder across multiple sites and denoising strategies , 2019 .

[94]  Lisa Byrge,et al.  Nonreplication of functional connectivity differences in autism spectrum disorder across multiple sites and denoising strategies , 2020, Human brain mapping.

[95]  M. Tribus,et al.  Probability theory: the logic of science , 2003 .

[96]  B. Franke,et al.  Individual differences v. the average patient: mapping the heterogeneity in ADHD using normative models , 2019, Psychological Medicine.

[97]  B. Yeo,et al.  Reconciling Dimensional and Categorical Models of Autism Heterogeneity: a Brain Connectomics & Behavioral Study , 2019, bioRxiv.

[98]  C. Beckmann,et al.  Conceptualizing mental disorders as deviations from normative functioning , 2019, Molecular Psychiatry.

[99]  Mark W. Woolrich,et al.  Multi-subject hierarchical inverse covariance modelling improves estimation of functional brain networks , 2018, NeuroImage.

[100]  Mark W. Woolrich,et al.  Linked independent component analysis for multimodal data fusion , 2011, NeuroImage.

[101]  R. T. Cox Probability, frequency and reasonable expectation , 1990 .

[102]  I. Rezek,et al.  Understanding Heterogeneity in Clinical Cohorts Using Normative Models: Beyond Case-Control Studies , 2016, Biological Psychiatry.

[103]  M. Breakspear,et al.  The connectomics of brain disorders , 2015, Nature Reviews Neuroscience.

[104]  Joseph Ramsey,et al.  Bayesian networks for fMRI: A primer , 2014, NeuroImage.

[105]  Mert R. Sabuncu,et al.  The influence of head motion on intrinsic functional connectivity MRI , 2012, NeuroImage.

[106]  Yarin Gal,et al.  Uncertainty in Deep Learning , 2016 .

[107]  P. Matthews,et al.  Multimodal population brain imaging in the UK Biobank prospective epidemiological study , 2016, Nature Neuroscience.

[108]  Jim Euchner,et al.  Spectrum Disorder , 2012 .

[109]  Karl J. Friston,et al.  Bayesian fMRI time series analysis with spatial priors , 2005, NeuroImage.

[110]  M. Seghier,et al.  Interpreting and Utilising Intersubject Variability in Brain Function , 2018, Trends in Cognitive Sciences.

[111]  Danilo Bzdok,et al.  Shared endo-phenotypes of default mode dysfunction in attention deficit/hyperactivity disorder and autism spectrum disorder , 2018, Translational Psychiatry.

[112]  Essa Yacoub,et al.  The WU-Minn Human Connectome Project: An overview , 2013, NeuroImage.

[113]  P. Bolton,et al.  Brief Report Prevalence of Autism Spectrum Conditions in Children Aged 5-11 Years in Cambridgeshire, UK , 2002, Autism : the international journal of research and practice.

[114]  Torrin M. Liddell,et al.  The Bayesian New Statistics: Hypothesis Testing, Estimation, Meta-Analysis, and Power Analysis from a Bayesian Perspective , 2016 .

[115]  Ruth A. Carper,et al.  Autism and Abnormal Development of Brain Connectivity , 2004, The Journal of Neuroscience.

[116]  Sylvie Goldman,et al.  Opinion: Sex, Gender and the Diagnosis of Autism - A Biosocial View of the Male Preponderance. , 2013, Research in autism spectrum disorders.

[117]  Simon Baron-Cohen,et al.  Quantifying and exploring camouflaging in men and women with autism , 2016, Autism : the international journal of research and practice.

[118]  Brian Caffo,et al.  A Bayesian hierarchical framework for spatial modeling of fMRI data , 2008, NeuroImage.

[119]  T. Ferguson A Bayesian Analysis of Some Nonparametric Problems , 1973 .

[120]  R. Kass,et al.  Approximate Bayesian Inference in Conditionally Independent Hierarchical Models (Parametric Empirical Bayes Models) , 1989 .

[121]  Karl J. Friston,et al.  Bayesian decoding of brain images , 2008, NeuroImage.