title: Gibbs distribution for statistical analysis of graphical data with a sample application to fcMRI brain images.
abstract: This paper develops object-oriented data analysis (OODA) statistical methods that are novel and complementary to existing methods of analysis of human brain scan connectomes, defined as graphs representing brain anatomical or functional connectivity. OODA is an emerging field where classical statistical approaches (e.g., hypothesis testing, regression, estimation, and confidence intervals) are applied to data objects such as graphs or functions. By analyzing data objects directly we avoid loss of information that occurs when data objects are transformed into numerical summary statistics. By providing statistical tools that analyze sets of connectomes without loss of information, new insights into neurology and medicine may be achieved. In this paper we derive the formula for statistical model fitting, regression, and mixture models; test their performance in simulation experiments; and apply them to connectomes from fMRI brain scans collected during a serial reaction time task study. Software for fitting graphical object-oriented data analysis is provided.
authors.affiliation: Department of Medicine, Washington University, St. Louis, MO, U.S.A.|Global IT Analytics, R&D, Monsanto Company, St. Louis, MO, U.S.A.
authors.forename: Patricio S
authors.initials: PS
authors.lastname: La Rosa
authors.affiliation: Department of Medicine, Washington University, St. Louis, MO, U.S.A.
authors.forename: Terrence L
authors.initials: TL
authors.lastname: Brooks
authors.affiliation: Department of Medicine, Washington University, St. Louis, MO, U.S.A.
authors.forename: Elena
authors.initials: E
authors.lastname: Deych
authors.affiliation: Department of Medicine, Washington University, St. Louis, MO, U.S.A.|BioRankings, LLC, St. Louis, MO, U.S.A.
authors.forename: Berkley
authors.initials: B
authors.lastname: Shands
authors.affiliation: Mallinckrodt Institute of Radiology, Washington University, St. Louis, MO, U.S.A.
authors.forename: Fred
authors.initials: F
authors.lastname: Prior
authors.affiliation: Mallinckrodt Institute of Radiology, Washington University, St. Louis, MO, U.S.A.|Department of Neurology, Washington University, St. Louis, MO, U.S.A.
authors.forename: Linda J
authors.initials: LJ
authors.lastname: Larson-Prior
authors.affiliation: Department of Medicine, Washington University, St. Louis, MO, U.S.A.|BioRankings, LLC, St. Louis, MO, U.S.A.
authors.forename: William D
authors.initials: WD
authors.lastname: Shannon
mesh_terms: D000328:Adult; D000465:Algorithms; D001921:Brain / Q000033:anatomy & histology / Q000502:physiology*; D016009:Chi-Square Distribution; D003198:Computer Simulation; D003627:Data Interpretation, Statistical; D005260:Female; D006801:Humans; D016013:Likelihood Functions; D008279:Magnetic Resonance Imaging; D008297:Male; D008875:Middle Aged; D009010:Monte Carlo Method; D011930:Reaction Time; D012984:Software
keywords: Gibbs model; biostatistics; connectomes; object-oriented data analysis