A markov chain monte carlo method for inverse stochastic modeling and uncertainty assessment

Unlike the traditional two-stage methods, a conditional and inverse-conditional simulation approach may directly generate independent, identically distributed realizations to honor both static data and state data in one step. The Markov chain Monte Carlo (McMC) method was proved a powerful tool to perform such type of stochastic simulation. One of the main advantages of the McMC over the traditional sensitivity-based optimization methods to inverse problems is its power, flexibility and well-posedness in incorporating observation data from different sources. In this work, an improved version of the McMC method is presented to perform the stochastic simulation of reservoirs and aquifers in the framework of multi-Gaussian geostatistics. First, a blocking scheme is proposed to overcome the limitations of the classic single-component Metropolis-Hastings-type McMC. One of the main characteristics of the blocking McMC (BMcMC) scheme is that, depending on the inconsistence between the prior model and the reality, it can preserve the prior spatial structure and statistics as users specified. At the same time, it improves the mixing of the Markov chain and hence enhances the computational efficiency of the McMC. Furthermore, the exploration ability and the mixing speed of McMC are efficiently improved by coupling the multiscale proposals, i.e., the coupled multiscale McMC method. In order to make the BMcMC method capable of dealing with the high-dimensional cases, a multi-scale scheme is introduced to accelerate the computation of the likelihood which greatly improves the computational efficiency of the McMC due to the fact that most of the computational efforts are spent on the forward simulations. To this end, a flexible-grid full-tensor finite-difference simulator, which is widely compatible with the outputs from various upscaling subroutines, is developed to solve the flow equations and a constant-displacement random-walk particle-tracking method, which enhances the comFu, J. (2008). A markov chain monte carlo method for inverse stochastic modeling and uncertainty assessment [Tesis doctoral no publicada]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/1969Palanci

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

Évaluation de la variabilité interindividuelle de la toxicocinétique de composés organiques volatils chez l'humain

Mémoire numérisé par la Division de la gestion de documents et des archives de l'Université de Montréal

The development of a convergence diagnostic for Markov Chain Monte Carlo estimation

The development and investigation of a convergence diagnostic for Markov Chain Monte Carlo (MCMC) posterior distributions is presented in this paper. The current method is an adaptation of an existing convergence diagnostic based on the Cumulative Sum (CUSUM, Page 1954; Yu & Mykland, 1998; Brooks, 1998c) procedure. The diagnostic under development is seen to be an improvement over the technique upon which it is based because it offers a simple way to remove one of the two major assumptions made by the previous method, namely that the shape of the distribution under consideration is symmetric. Results are mixed, but there is some evidence to indicate that the new technique is sensitive to the degree of autocorrelation present and the stability of the chains. Also, the new diagnostic behaves differently than three existing convergence diagnostics

Change-point Problem and Regression: An Annotated Bibliography

The problems of identifying changes at unknown times and of estimating the location of changes in stochastic processes are referred to as the change-point problem or, in the Eastern literature, as disorder . The change-point problem, first introduced in the quality control context, has since developed into a fundamental problem in the areas of statistical control theory, stationarity of a stochastic process, estimation of the current position of a time series, testing and estimation of change in the patterns of a regression model, and most recently in the comparison and matching of DNA sequences in microarray data analysis. Numerous methodological approaches have been implemented in examining change-point models. Maximum-likelihood estimation, Bayesian estimation, isotonic regression, piecewise regression, quasi-likelihood and non-parametric regression are among the methods which have been applied to resolving challenges in change-point problems. Grid-searching approaches have also been used to examine the change-point problem. Statistical analysis of change-point problems depends on the method of data collection. If the data collection is ongoing until some random time, then the appropriate statistical procedure is called sequential. If, however, a large finite set of data is collected with the purpose of determining if at least one change-point occurred, then this may be referred to as non-sequential. Not surprisingly, both the former and the latter have a rich literature with much of the earlier work focusing on sequential methods inspired by applications in quality control for industrial processes. In the regression literature, the change-point model is also referred to as two- or multiple-phase regression, switching regression, segmented regression, two-stage least squares (Shaban, 1980), or broken-line regression. The area of the change-point problem has been the subject of intensive research in the past half-century. The subject has evolved considerably and found applications in many different areas. It seems rather impossible to summarize all of the research carried out over the past 50 years on the change-point problem. We have therefore confined ourselves to those articles on change-point problems which pertain to regression. The important branch of sequential procedures in change-point problems has been left out entirely. We refer the readers to the seminal review papers by Lai (1995, 2001). The so called structural change models, which occupy a considerable portion of the research in the area of change-point, particularly among econometricians, have not been fully considered. We refer the reader to Perron (2005) for an updated review in this area. Articles on change-point in time series are considered only if the methodologies presented in the paper pertain to regression analysis

Analysis of Heterogeneous Data Sources for Veterinary Syndromic Surveillance to Improve Public Health Response and Aid Decision Making

The standard technique of implementing veterinary syndromic surveillance (VSyS) is the detection of temporal or spatial anomalies in the occurrence of health incidents above a set threshold in an observed population using the Frequentist modelling approach. Most implementation of this technique also requires the removal of historical outbreaks from the datasets to construct baselines. Unfortunately, some challenges exist, such as data scarcity, delayed reporting of health incidents, and variable data availability from sources, which make the VSyS implementation and alarm interpretation difficult, particularly when quantifying surveillance risk with associated uncertainties. This problem indicates that alternate or improved techniques are required to interpret alarms when incorporating uncertainties and previous knowledge of health incidents into the model to inform decision-making. Such methods must be capable of retaining historical outbreaks to assess surveillance risk. In this research work, the Stochastic Quantitative Risk Assessment (SQRA) model was proposed and developed for detecting and quantifying the risk of disease outbreaks with associated uncertainties using the Bayesian probabilistic approach in PyMC3. A systematic and comparative evaluation of the available techniques was used to select the most appropriate method and software packages based on flexibility, efficiency, usability, ability to retain historical outbreaks, and the ease of developing a model in Python. The social media datasets (Twitter) were first applied to infer a possible disease outbreak incident with associated uncertainties. Then, the inferences were subsequently updated using datasets from the clinical and other healthcare sources to reduce uncertainties in the model and validate the outbreak. Therefore, the proposed SQRA model demonstrates an approach that uses the successive refinement of analysis of different data streams to define a changepoint signalling a disease outbreak. The SQRA model was tested and validated to show the method's effectiveness and reliability for differentiating and identifying risk regions with corresponding changepoints to interpret an ongoing disease outbreak incident. This demonstrates that a technique such as the SQRA method obtained through this research may aid in overcoming some of the difficulties identified in VSyS, such as data scarcity, delayed reporting, and variable availability of data from sources, ultimately contributing to science and practice