Temporal gene expression data have been studied and applied in biological, biomedical studies and early cancer detection. A set of temporal gene expression data in bacteria shows that the gene expression has different patterns under different biological conditions. The datasets are treated as functional data in this study, and the goal of my search is to detect outliers based on functional data theory. Then, we can identify the biological conditions that produce outliers and provide valuable information for biologists to find treatment to the bacteria. The datasets with 21 genes in P. Aeruginosa expressed in 24 biological conditions have been studied in this thesis. The aim of my research is to find the in uence of the biological conditions to each gene as we can visually find a few curves are significantly different from others, but they are supposed to have the same distribution as the rest curves. Therefore, we detect the conditions that produce outliers in each gene. We apply four functional depth notions, the Fraiman and Muniz depth, the h-modal depth, the random projection depth, and the random Tukey depth.

The simulation experiments to the outlier detection procedures are conducted accordingly and it performs well. Then, we apply the outlier detection procedures to the 21 genes datasets. In terms of the performance of each depth, the outlier detection results resemble the simulation results. We have identified the conditions that produce outliers of gene trajectories, and the results agree well with the classification of biological conditions result based on minimum Mahalanobis distance.