Robust Uncertainty Quantification and Scalable Computation for Computer Models with Massive Output

Uncertainty quantification (UQ) is both an old and new concept. The current novelty lies in the interactions and synthesis of mathematical models, computer experiments, statistics, field/real experiments, and probability theory, with a particular emphasize on the large-scale simulations by computer models. The challenges not only come from the complication of scientific questions, but also from the size of the information. It is the focus in this thesis to provide statistical models that are scalable to massive data produced in computer experiments and real experiments, through fast and robust statistical inference.

Chapter 2 provides a practical approach for simultaneously emulating/approximating massive number of functions, with the application on hazard quantification of Soufri\`{e}re Hills volcano in Montserrate island. Chapter 3 discusses another problem with massive data, in which the number of observations of a function is large. An exact algorithm that is linear in time is developed for the problem of interpolation of Methylation levels. Chapter 4 and Chapter 5 are both about the robust inference of the models. Chapter 4 provides a new criteria robustness parameter estimation criteria and several ways of inference have been shown to satisfy such criteria. Chapter 5 develops a new prior that satisfies some more criteria and is thus proposed to use in practice.

Predicting Transcript Production Rates in Yeast With Sparse Linear Models

To provide biological insights into transcriptional regulation, a couple of groups have recently presented models relating the promoter DNA-bound transcription factors (TFs) to downstream gene’s mean transcript level or transcript production rates over time. However, transcript production is dynamic in response to changes of TF concentrations over time. Also, TFs are not the only factors binding to promoters; other DNA binding factors (DBFs) bind as well, especially nucleosomes, resulting in competition between DBFs for binding at same genomic location. Additionally, not only TFs, but also some other elements regulate transcription. Within core promoter, various regulatory elements influence RNAPII recruitment, PIC formation, RNAPII searching for TSS, and RNAPII initiating transcription. Moreover, it is proposed that downstream from TSS, nucleosomes resist RNAPII elongation.

Here, we provide a machine learning framework to predict transcript production rates from DNA sequences. We applied this framework in the S. cerevisiae yeast for two scenarios: a) to predict the dynamic transcript production rate during the cell cycle for native promoters; b) to predict the mean transcript production rate over time for synthetic promoters. As far as we know, our framework is the first successful attempt to have a model that can predict dynamic transcript production rates from DNA sequences only: with cell cycle data set, we got Pearson correlation coefficient Cp = 0.751 and coefficient of determination r2 = 0.564 on test set for predicting dynamic transcript production rate over time. Also, for DREAM6 Gene Promoter Expression Prediction challenge, our fitted model outperformed all participant teams, best of all teams, and a model combining best team’s k-mer based sequence features and another paper’s biologically mechanistic features, in terms of all scoring metrics.

Moreover, our framework shows its capability of identifying generalizable fea- tures by interpreting the highly predictive models, and thereby provide support for associated hypothesized mechanisms about transcriptional regulation. With the learned sparse linear models, we got results supporting the following biological insights: a) TFs govern the probability of RNAPII recruitment and initiation possibly through interactions with PIC components and transcription cofactors; b) the core promoter amplifies the transcript production probably by influencing PIC formation, RNAPII recruitment, DNA melting, RNAPII searching for and selecting TSS, releasing RNAPII from general transcription factors, and thereby initiation; c) there is strong transcriptional synergy between TFs and core promoter elements; d) the regulatory elements within core promoter region are more than TATA box and nucleosome free region, suggesting the existence of still unidentified TAF-dependent and cofactor-dependent core promoter elements in yeast S. cerevisiae; e) nucleosome occupancy is helpful for representing +1 and -1 nucleosomes’ regulatory roles on transcription.