The Annals of Applied Statistics

A Markov random field-based approach to characterizing human brain development using spatial–temporal transcriptome data

Zhixiang Lin, Stephan J. Sanders, Mingfeng Li, Nenad Sestan, Matthew W. State, and Hongyu Zhao

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Human neurodevelopment is a highly regulated biological process. In this article, we study the dynamic changes of neurodevelopment through the analysis of human brain microarray data, sampled from 16 brain regions in 15 time periods of neurodevelopment. We develop a two-step inferential procedure to identify expressed and unexpressed genes and to detect differentially expressed genes between adjacent time periods. Markov Random Field (MRF) models are used to efficiently utilize the information embedded in brain region similarity and temporal dependency in our approach. We develop and implement a Monte Carlo expectation–maximization (MCEM) algorithm to estimate the model parameters. Simulation studies suggest that our approach achieves lower misclassification error and potential gain in power compared with models not incorporating spatial similarity and temporal dependency.

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Ann. Appl. Stat., Volume 9, Number 1 (2015), 429-451.

First available in Project Euclid: 28 April 2015

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Markov Random Field model spatial and temporal data neurodevelopment microarray Monte Carlo expectation–maximization algorithm gene expression differential expression


Lin, Zhixiang; Sanders, Stephan J.; Li, Mingfeng; Sestan, Nenad; State, Matthew W.; Zhao, Hongyu. A Markov random field-based approach to characterizing human brain development using spatial–temporal transcriptome data. Ann. Appl. Stat. 9 (2015), no. 1, 429--451. doi:10.1214/14-AOAS802.

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Supplemental materials

  • Supplement to "A Markov random field-based approach to characterizing human brain development using spatial-temporal transcriptome data".: Section 1: More information on the brain regions. Section 2: Spatial and temporal similarity. Section 3: Microarray quality control procedures. Section 4: Model fit and the robustness of the Gaussian mixture model. Section 5: Diagnosis for the MCEM algorithm. Section 6: Gene Ontology (GO) enrichment analysis. Section 7: High confidence ASD genes. Section 8: Supplementary data for Section 4.1. Section 9: Supplementary data for Section 4.2. Section 10: Comparison between the ICM algorithm and the MCEM algorithm.