Gaussian graphical modeling for spectrometric data analysis

Motivated by the analysis of spectrometric data, we introduce a Gaussian graphical model for learning the dependence structure among frequency bands of the infrared absorbance spectrum. The spectra are modeled as continuous functional data through a B-spline basis expansion and a Gaussian graphical model is assumed as a prior specification for the smoothing coefficients to induce sparsity in their precision matrix. Bayesian inference is carried out to simultaneously smooth the curves and to estimate the conditional independence structure between portions of the functional domain. The proposed model is applied to the analysis of infrared absorbance spectra of strawberry purees.

[1]  E. K. Kemsley,et al.  Detection of adulteration of raspberry purees using infrared spectroscopy and chemometrics , 1996 .

[2]  E. K. Kemsley,et al.  Near- and Mid-Infrared Spectroscopies in Food Authentication: Coffee Varietal Identification , 1997 .

[3]  Alex Lenkoski,et al.  A direct sampler for G‐Wishart variates , 2013, 1304.1350.

[4]  C. Preston.  Spatial birth and death processes , 1975, Advances in Applied Probability.

[5]  H. Rue,et al.  An explicit link between Gaussian fields and Gaussian Markov random fields: the stochastic partial differential equation approach , 2011 .

[6]  R. A. Leibler,et al.  On Information and Sufficiency , 1951 .

[7]  E. R. Morrissey,et al.  Inferring the time-invariant topology of a nonlinear sparse gene regulatory network using fully Bayesian spline autoregression. , 2011, Biostatistics.

[8]  A. Roverato.  Hyper Inverse Wishart Distribution for Non-decomposable Graphs and its Application to Bayesian Inference for Gaussian Graphical Models , 2002 .

[9]  E. K. Kemsley,et al.  Use of Fourier transform infrared spectroscopy and partial least squares regression for the detection of adulteration of strawberry purées , 1998 .

[10]  O. G. Meza-Márquez,et al.  Application of mid-infrared spectroscopy with multivariate analysis and soft independent modeling of class analogies (SIMCA) for the detection of adulterants in minced beef. , 2010, Meat science.

[11]  Jian Kang,et al.  Bayesian Network Marker Selection via the Thresholded Graph Laplacian Gaussian Prior. , 2018, Bayesian analysis.

[12]  Francesco C Stingo,et al.  Bayesian nonlinear model selection for gene regulatory networks , 2015, Biometrics.

[13]  Paolo Giudici,et al.  Improving Markov Chain Monte Carlo Model Search for Data Mining , 2004, Machine Learning.

[14]  Bani K Mallick,et al.  Joint High‐Dimensional Bayesian Variable and Covariance Selection with an Application to eQTL Analysis , 2013, Biometrics.

[15]  Constantin F. Aliferis,et al.  The max-min hill-climbing Bayesian network structure learning algorithm , 2006, Machine Learning.

[16]  Marina Vannucci,et al.  Hierarchical Normalized Completely Random Measures for Robust Graphical Modeling. , 2019, Bayesian analysis.

[17]  James G. Scott,et al.  Feature-Inclusion Stochastic Search for Gaussian Graphical Models , 2008 .

[18]  Christine B Peterson,et al.  Joint Bayesian variable and graph selection for regression models with network‐structured predictors , 2016, Statistics in medicine.

[19]  A. Tielens,et al.  The infrared emission bands. I - Correlation studies and the dependence on C/O ratio. [in planetary and reflection nebulae and H II regions] , 1986 .

[20]  Jingjing Yang,et al.  Smoothing and Mean-Covariance Estimation of Functional Data with a Bayesian Hierarchical Model. , 2014, Bayesian analysis.

[21]  Kenneth Rice,et al.  FDR and Bayesian Multiple Comparisons Rules , 2006 .

[22]  David B. Dunson,et al.  Bayesian Graphical Models for Multivariate Functional Data , 2014, J. Mach. Learn. Res..

[23]  Hao Wang,et al.  Sparse seemingly unrelated regression modelling: Applications in finance and econometrics , 2010, Comput. Stat. Data Anal..

[24]  T. Fearn,et al.  Bayesian Wavelet Regression on Curves With Application to a Spectroscopic Calibration Problem , 2001 .

[25]  Luo Xiao,et al.  Fast covariance estimation for high-dimensional functional data , 2013, Stat. Comput..

[26]  Fei Liu,et al.  B Selected variables in KPI data analysis , 2010 .

[27]  G'erard Letac,et al.  Wishart distributions for decomposable graphs , 2007, 0708.2380.

[28]  Ciprian M Crainiceanu,et al.  Bayesian Functional Data Analysis Using WinBUGS. , 2010, Journal of statistical software.

[29]  Aurelie C. Lozano,et al.  A graph Laplacian prior for Bayesian variable selection and grouping , 2019, Comput. Stat. Data Anal..

[30]  Michael A. West,et al.  Archival Version including Appendicies : Experiments in Stochastic Computation for High-Dimensional Graphical Models , 2005 .

[31]  Christine B Peterson,et al.  Bayesian Inference of Multiple Gaussian Graphical Models , 2015, Journal of the American Statistical Association.

[32]  Caroline Uhler,et al.  Exact formulas for the normalizing constants of Wishart distributions for graphical models , 2014, 1406.4901.

[33]  S. Lang,et al.  Bayesian P-Splines , 2004 .

[34]  Xinghao Qiao,et al.  Functional Graphical Models , 2018, Journal of the American Statistical Association.

[35]  M. West,et al.  Sparse graphical models for exploring gene expression data , 2004 .

[36]  Wenyang Zhang,et al.  Estimating the covariance function with functional data. , 2002, The British journal of mathematical and statistical psychology.

[37]  Yang Ni,et al.  Sparse Multi-Dimensional Graphical Models: A Unified Bayesian Framework , 2017 .

[38]  O. Cappé,et al.  Reversible jump, birth‐and‐death and more general continuous time Markov chain Monte Carlo samplers , 2003 .

[39]  Xinghao Qiao,et al.  Doubly functional graphical models in high dimensions , 2020, Biometrika.

[40]  Lucia Paci,et al.  Structural learning of contemporaneous dependencies in graphical VAR models , 2020, Comput. Stat. Data Anal..

[41]  Maria De Iorio,et al.  Bayesian inference for multiple Gaussian graphical models with application to metabolic association networks , 2016, 1603.06358.

[42]  Dennis D. Cox,et al.  Efficient Bayesian hierarchical functional data analysis with basis function approximations using Gaussian–Wishart processes , 2015, Biometrics.

[43]  J. Berger,et al.  Optimal predictive model selection , 2004, math/0406464.

[44]  B. Li,et al.  A Nonparametric Graphical Model for Functional Data With Application to Brain Networks Based on fMRI , 2018, Journal of the American Statistical Association.

[45]  Abdolreza Mohammadi,et al.  BDgraph: An R Package for Bayesian Structure Learning in Graphical Models , 2015, Journal of Statistical Software.

[46]  Lurdes Y. T. Inoue,et al.  Bayesian Hierarchical Curve Registration , 2008 .

[47]  Jingjing Yang,et al.  BFDA: A Matlab Toolbox for Bayesian Functional Data Analysis , 2016 .

[48]  A. Mohammadi,et al.  Bayesian Structure Learning in Sparse Gaussian Graphical Models , 2012, 1210.5371.

[49]  Hans-Georg Müller,et al.  Functional Data Analysis , 2016 .

[50]  Alessia Pini,et al.  The interval testing procedure: A general framework for inference in functional data analysis , 2016, Biometrics.