A ROBUST B AYESIAN TWO - SAMPLE TEST FOR DETECTING INTERVALS OF DIFFERENTIAL GENE EXPRESSION IN MICROARRAY TIME SERIES Oliver Stegle, Katherine Denby,

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A ROBUST B AYESIAN TWO - SAMPLE TEST FOR DETECTING INTERVALS OF DIFFERENTIAL GENE EXPRESSION IN MICROARRAY TIME SERIES Oliver Stegle, Katherine Denby, David L. Wild, Zoubin Ghahramani, Karsten M. Borgwardt Journal of Computational Biology 1 VC Lab, Dept. of Computer Science, NTHU, Taiwan

O VERVIEW Introduction Differential Expression Method and Model Bayesian network Score Gaussian process Experiment Conclusion Reference 2 VC Lab, Dept. of Computer Science, NTHU, Taiwan

I NTRODUCTION Differential Expression Distribution is defined by mean and stdv. Significant change in mean of measurements Methods SAM(Significance analysis of microarrays) T-test Whether / When 3 VC Lab, Dept. of Computer Science, NTHU, Taiwan oint___Differential_Expression.ppt.pdf oint___Differential_Expression.ppt.pdf

M ETHOD AND M ODELS Bayesian network 4 VC Lab, Dept. of Computer Science, NTHU, Taiwan

M ETHOD AND M ODELS Score Logarithm of the Bayes factor 5 VC Lab, Dept. of Computer Science, NTHU, Taiwan Observed expression levels Gaussian process models Hyperparameters I: independent S: shared

M ETHOD AND M ODELS Gaussian process Robustness Detect true differential expression 6 VC Lab, Dept. of Computer Science, NTHU, Taiwan Global noise Covariance matrix Latent replicate observations Pre-replicate noise set of all hyperparameters for kernel, likelihood and the replicate noise levels.

M ETHOD AND M ODELS Gaussian process (Cont.) Simplify 7 VC Lab, Dept. of Computer Science, NTHU, Taiwan variance of observation noise

M ETHOD AND M ODELS Gaussian process (Cont.) Gaussian predictive distribution Bayes factor Most probable parameter (from posterior probbility) 8 VC Lab, Dept. of Computer Science, NTHU, Taiwan characteristic function

M ETHOD AND M ODELS Gaussian process (Cont.) Robustness with respect to outliers Mixture model Expectation Propagation(EP) Update one factor, leave others fixed. 9 VC Lab, Dept. of Computer Science, NTHU, Taiwan Probability of being a regular observation Probability of being a outlier

E XPERIMENT Differential gene expression in Arabidopsis thaliana after fungal infection Botrytis cinerea 10 VC Lab, Dept. of Computer Science, NTHU, Taiwan A rea u nder the c urve T ime c ourse method

E XPERIMENT Detecting intervals of differential gene expression Bernoulli distribution 11 VC Lab, Dept. of Computer Science, NTHU, Taiwan

R ESULTS 12 VC Lab, Dept. of Computer Science, NTHU, Taiwan

R ESULTS 13 VC Lab, Dept. of Computer Science, NTHU, Taiwan

C ONCLUSION Detecting differential gene expression Gaussian process framework When Regulatory network 14 VC Lab, Dept. of Computer Science, NTHU, Taiwan

R EFERENCE Ziv Bar-Joseph et al., Cross Species Expression Analysis of Innate Immune Response, Journal of Computational Biology 355~367, March, _PowerPoint___Differential_Expression.ppt.pdf _PowerPoint___Differential_Expression.ppt.pdf 15 VC Lab, Dept. of Computer Science, NTHU, Taiwan