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Fully Bayesian Mixture Model for Differential Gene Expression: Simulations and Model Checks

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  • Lewin Alex

    (Imperial, London)

  • Bochkina Natalia

    (The University of Edinburgh)

  • Richardson Sylvia

    (Imperial, London)

Abstract

We present a Bayesian hierarchical model for detecting differentially expressed genes using a mixture prior on the parameters representing differential effects. We formulate an easily interpretable 3-component mixture to classify genes as over-expressed, under-expressed and non-differentially expressed, and model gene variances as exchangeable to allow for variability between genes. We show how the proportion of differentially expressed genes, and the mixture parameters, can be estimated in a fully Bayesian way, extending previous approaches where this proportion was fixed and empirically estimated. Good estimates of the false discovery rates are also obtained.Different parametric families for the mixture components can lead to quite different classifications of genes for a given data set. Using Affymetrix data from a knock out and wildtype mice experiment, we show how predictive model checks can be used to guide the choice between possible mixture priors. These checks show that extending the mixture model to allow extra variability around zero instead of the usual point mass null fits the data better.A software package for R is available.

Suggested Citation

  • Lewin Alex & Bochkina Natalia & Richardson Sylvia, 2007. "Fully Bayesian Mixture Model for Differential Gene Expression: Simulations and Model Checks," Statistical Applications in Genetics and Molecular Biology, De Gruyter, vol. 6(1), pages 1-28, December.
    • Handle: RePEc:bpj:sagmbi:v:6:y:2007:i:1:n:36
    DOI: 10.2202/1544-6115.1314
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    Cited by:

    1. Alfo' Marco & Farcomeni Alessio & Tardella Luca, 2011. "A Three Component Latent Class Model for Robust Semiparametric Gene Discovery," Statistical Applications in Genetics and Molecular Biology, De Gruyter, vol. 10(1), pages 1-19, January.
    2. Zoé van Havre & Nicole White & Judith Rousseau & Kerrie Mengersen, 2015. "Overfitting Bayesian Mixture Models with an Unknown Number of Components," PLOS ONE, Public Library of Science, vol. 10(7), pages 1-27, July.
    3. Vinícius Diniz Mayrink & Flávio Bambirra Gonçalves, 2017. "A Bayesian hidden Markov mixture model to detect overexpressed chromosome regions," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 66(2), pages 387-412, February.
    4. Vinícius Diniz Mayrink & Flávio B. Gonçalves, 2020. "Identifying atypically expressed chromosome regions using RNA-Seq data," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 29(3), pages 619-649, September.

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