Bayesian treed multivariate Gaussian process with adaptive design: Application to a carbon capture unit

Computer experiments are widely used in scientific research to study and predict the behavior of complex systems, which often have responses consisting of a set of nonstationary outputs. The computational cost of simulations at high resolution often is expensive and impractical for parametric studies at different input values. In this article, we develop a Bayesian treed multivariate Gaussian process (BTMGP) as an extension of the Bayesian treed Gaussian process (BTGP) to model the cross-covariance function and the nonstationarity of the multivariate output. We facilitate the computational complexity of the Markov chain Monte Carlo sampler by choosing appropriately the covariance function and prior distributions. Based on the BTMGP, we develop a sequential design of experiment for the input space and construct an emulator. We demonstrate the use of the proposed method in test cases and compare it with alternative approaches. We also apply the sequential sampling technique and BTMGP to model the multiphase flow in a full scale regenerator of a carbon capture unit

Efficient, concurrent Bayesian analysis of full waveform LaDAR data

Bayesian analysis of full waveform laser detection and ranging (LaDAR) signals using reversible jump Markov chain Monte Carlo (RJMCMC) algorithms have shown higher estimation accuracy, resolution and sensitivity to detect weak signatures for 3D surface profiling, and construct multiple layer images with varying number of surface returns. However, it is computational expensive. Although parallel computing has the potential to reduce both the processing time and the requirement for persistent memory storage, parallelizing the serial sampling procedure in RJMCMC is a significant challenge in both statistical and computing domains. While several strategies have been developed for Markov chain Monte Carlo (MCMC) parallelization, these are usually restricted to fixed dimensional parameter estimates, and not obviously applicable to RJMCMC for varying dimensional signal analysis. In the statistical domain, we propose an effective, concurrent RJMCMC algorithm, state space decomposition RJMCMC (SSD-RJMCMC), which divides the entire state space into groups and assign to each an independent RJMCMC chain with restricted variation of model dimensions. It intrinsically has a parallel structure, a form of model-level parallelization. Applying the convergence diagnostic, we can adaptively assess the convergence of the Markov chain on-the-fly and so dynamically terminate the chain generation. Evaluations on both synthetic and real data demonstrate that the concurrent chains have shorter convergence length and hence improved sampling efficiency. Parallel exploration of the candidate models, in conjunction with an error detection and correction scheme, improves the reliability of surface detection. By adaptively generating a complimentary MCMC sequence for the determined model, it enhances the accuracy for surface profiling. In the computing domain, we develop a data parallel SSD-RJMCMC (DP SSD-RJMCMCU) to achieve efficient parallel implementation on a distributed computer cluster. Adding data-level parallelization on top of the model-level parallelization, it formalizes a task queue and introduces an automatic scheduler for dynamic task allocation. These two strategies successfully diminish the load imbalance that occurred in SSD-RJMCMC. Thanks to the coarse granularity, the processors communicate at a very low frequency. The MPIbased implementation on a Beowulf cluster demonstrates that compared with RJMCMC, DP SSD-RJMCMCU has further reduced problem size and computation complexity. Therefore, it can achieve a super linear speedup if the number of data segments and processors are chosen wisely

A Simplified Crossing Fiber Model in Diffusion Weighted Imaging

Diffusion MRI (dMRI) is a vital source of imaging data for identifying anatomical connections in the living human brain that form the substrate for information transfer between brain regions. dMRI can thus play a central role toward our understanding of brain function. The quantitative modeling and analysis of dMRI data deduces the features of neural fibers at the voxel level, such as direction and density. The modeling methods that have been developed range from deterministic to probabilistic approaches. Currently, the Ball-and-Stick model serves as a widely implemented probabilistic approach in the tractography toolbox of the popular FSL software package and FreeSurfer/TRACULA software package. However, estimation of the features of neural fibers is complex under the scenario of two crossing neural fibers, which occurs in a sizeable proportion of voxels within the brain. A Bayesian non-linear regression is adopted, comprised of a mixture of multiple non-linear components. Such models can pose a difficult statistical estimation problem computationally. To make the approach of Ball-and-Stick model more feasible and accurate, we propose a simplified version of Ball-and-Stick model that reduces parameter space dimensionality. This simplified model is vastly more efficient in the terms of computation time required in estimating parameters pertaining to two crossing neural fibers through Bayesian simulation approaches. Moreover, the performance of this new model is comparable or better in terms of bias and estimation variance as compared to existing models

Markov chain Monte Carlo methods for parameter identification in systems biology models

First, I would like to thank Prof. Dr. Achim Tresch for giving me the opportunity to write this thesis and to work on three fascinating projects. I really appreciate all the fruitful discussions, his constant support and the excellent working atmosphere. I would also like to thank Prof. Dr. Patrick Cramer for being my doctoral supervisor. Furthermore, I would like to thank all the other members of my dissertation committee (Prof. Dr. Rainer Spang