We develop an approach for Bayesian learning of spatiotemporal dynamical mechanistic models. Such learning consists of statistical emulation of the mechanistic system that can efficiently interpolate the output of the system from arbitrary inputs. The emulated learner can then be used to train the system from noisy data achieved by melding information from observed data with the emulated mechanistic system. This joint melding of mechanistic systems employ hierarchical state-space models with Gaussian process regression. Assuming the dynamical system is controlled by a finite collection of inputs, Gaussian process regression learns the effect of these parameters through a number of training runs, driving the stochastic innovations of the spatiotemporal state-space component. This enables efficient modeling of the dynamics over space and time. This article details exact inference with analytically accessible posterior distributions in hierarchical matrix-variate Normal and Wishart models in designing the emulator. This step obviates expensive iterative algorithms such as Markov chain Monte Carlo or variational approximations. We also show how emulation is applicable to large-scale emulation by designing a dynamic Bayesian transfer learning framework. Inference on mechanistic model parameters proceeds using Markov chain Monte Carlo as a post-emulation step using the emulator as a regression component. We demonstrate this framework through solving inverse problems arising in the analysis of ordinary and partial nonlinear differential equations and, in addition, to a black-box computer model generating spatiotemporal dynamics across a graphical model.

Cancer is an abnormal division of cells and can spread to multiple tissues. Race has been reported as a determining factor in cancer susceptibility and, therefore, survival rate. The risks of malignancies among individuals of African ancestry and Asians compared to Caucasians are reported to be distinctive. Genetic factors due to mutations in DNA have been linked to the cause of specific cancer types and could play a key role in the survival of cancer patients. The Cancer Genome Atlas (TCGA) is a project initiated by the National Cancer Institute with the goal of characterizing genetic patterns for 34 cancer types/subtypes.By processing the genome sequencing datasets of TCGA cancers, we calculated the number of mutated genes (mutation frequency) for each TCGA cancer type and selected top five cancers based on the count of the uniquely mutated genes in cancer patients of different ethnicities. We then identified overlapping genes through conducting proportion tests for their mutation frequencies between races in each of selected cancers to look for evidence of racial disparity. Lastly, we performed functional annotation, key pathway analyses, and protein conserved domain detection for uniquely mutated genes between races.Our study revealed key cancer pathways and protein domains of identified driver genes contributing to the disparity in mortality rates between races. We developed a bioinformatics pipeline method for comparing survival disparities between races of TCGA cancers, which is deployed in the Google Colab notebook. The research findings from our study could offer racial-specific therapy recommendations for various malignancies.)