Improving Simulation Efficiency of MCMC for Inverse Modeling of Hydrologic Systems with a Kalman-Inspired Proposal Distribution

Bayesian analysis is widely used in science and engineering for real-time forecasting, decision making, and to help unravel the processes that explain the observed data. These data are some deterministic and/or stochastic transformations of the underlying parameters. A key task is then to summarize the posterior distribution of these parameters. When models become too difficult to analyze analytically, Monte Carlo methods can be used to approximate the target distribution. Of these, Markov chain Monte Carlo (MCMC) methods are particularly powerful. Such methods generate a random walk through the parameter space and, under strict conditions of reversibility and ergodicity, will successively visit solutions with frequency proportional to the underlying target density. This requires a proposal distribution that generates candidate solutions starting from an arbitrary initial state. The speed of the sampled chains converging to the target distribution deteriorates rapidly, however, with increasing parameter dimensionality. In this paper, we introduce a new proposal distribution that enhances significantly the efficiency of MCMC simulation for highly parameterized models. This proposal distribution exploits the cross-covariance of model parameters, measurements and model outputs, and generates candidate states much alike the analysis step in the Kalman filter. We embed the Kalman-inspired proposal distribution in the DREAM algorithm during burn-in, and present several numerical experiments with complex, high-dimensional or multi-modal target distributions. Results demonstrate that this new proposal distribution can greatly improve simulation efficiency of MCMC. Specifically, we observe a speed-up on the order of 10-30 times for groundwater models with more than one-hundred parameters

Modeling and forecasting riverine dissolved inorganic nitrogen export using anthropogenic nitrogen inputs, hydroclimate, and land-use change

A quantitative understanding of riverine nitrogen (N) export in response to human activities and climate change is critical for developing effective watershed N pollution control measures. This study quantified net anthropogenic N inputs (NANI) and riverine dissolved inorganic N (DIN=NO3-N+NH4-N+NO2-N) export for the upper Jiaojiang River catchment in eastern China over the 1980-2010 time period and examined how NANI, hydroclimate, and land-use practices influenced riverine DIN export. Over the 31-yr study period, riverine DIN yield increased by 1.6-fold, which mainly results from a ~77% increase in NANI and increasing fractional delivery of NANI due to a ~55% increase in developed land area. An empirical model that utilizes an exponential function of NANI and a power function of combining annual water discharge and developed land area percentage could account for 89% of the variation in annual riverine DIN yields in 1980-2010. Applying this model, annual NANI, catchment storage, and natural background sources were estimated to contribute 57%, 22%, and 21%, respectively, of annual riverine DIN exports on average. Forecasting based on a likely future climate change scenario predicted a 19.6% increase in riverine DIN yield by 2030 due to a 4% increase in annual discharge with no changes in NANI and land-use compared to the 2000-2010 baseline condition. Anthropogenic activities have increased both the N inputs available for export and the fractional export of N inputs, while climate change can further enhance riverine N export. An integrated N management strategy that considers the influence of anthropogenic N inputs, land-use and climate change is required to effectively control N inputs to coastal areas

Analysis of differential gene expression based on Bayesian estimation of variance

Gene expression is arguably the most important indicator of biological function. Thus identifying differentially expressed genes is one of the main aims of high throughout studies that use microarray and RNAseq platforms to study deregulated cellular pathways. There are many tools for analysing differentia gene expression from transciptomic datasets. The major challenge of this topic is to estimate gene expression variance due to the high amount of ‘background noise’ that is generated from biological equipment and the lack of biological replicates. Bayesian inference has been widely used in the bioinformatics field. In this work, we reveal that the prior knowledge employed in the Bayesian framework also helps to improve the accuracy of differential gene expression analysis when using a small number of replicates. We have developed a differential analysis tool that uses Bayesian estimation of the variance of gene expression for use with small numbers of biological replicates. Our method is more consistent when compared to the widely used cyber-t tool that successfully introduced the Bayesian framework to differential analysis. We also provide a user-friendly web based Graphic User Interface for biologists to use with microarray and RNAseq data. Bayesian inference can compensate for the instability of variance caused when using a small number of biological replicates by using pseudo replicates as prior knowledge. We also show that our new strategy to select pseudo replicates will improve the performance of the analysis. - See more at: http://www.eurekaselect.com/node/138761/article#sthash.VeK9xl5k.dpu

Improving Simulation Efficiency of MCMC for Inverse Modeling of Hydrologic Systems With a Kalman-Inspired Proposal Distribution

Bayesian analysis is widely used in science and engineering for real-time forecasting, decision making, and to help unravel the processes that explain the observed data. These data are some deterministic and/or stochastic transformations of the underlying parameters. A key task is then to summarize the posterior distribution of these parameters. When models become too difficult to analyze analytically, Monte Carlo methods can be used to approximate the target distribution. Of these, Markov chain Monte Carlo (MCMC) methods are particularly powerful. Such methods generate a random walk through the parameter space and, under strict conditions of reversibility and ergodicity, will successively visit solutions with frequency proportional to the underlying target density. This requires a proposal distribution that generates candidate solutions starting from an arbitrary initial state. The speed of the sampled chains converging to the target distribution deteriorates rapidly, however, with increasing parameter dimensionality. In this paper, we introduce a new proposal distribution that enhances significantly the efficiency of MCMC simulation for highly parameterized models. This proposal distribution exploits the cross-covariance of model parameters, measurements and model outputs, and generates candidate states much alike the analysis step in the Kalman filter. We embed the Kalman-inspired proposal distribution in the DREAM algorithm during burn-in, and present several numerical experiments with complex, high-dimensional or multi-modal target distributions. Results demonstrate that this new proposal distribution can greatly improve simulation efficiency of MCMC. Specifically, we observe a speed-up on the order of 10-30 times for groundwater models with more than one-hundred parameters

Long-Term (1990–2013) Changes and Spatial Variations of Cropland Runoff across China

Quantitative information on regional cropland runoff is important for sustainable agricultural water quantity and quality management. This study combined the Soil Conservation Service Curve Number (SCS-CN) method and geostatistical approaches to quantify long-term (1990–2013) changes and regional spatial variations of cropland runoff in China. Estimated CN values from 17 cropland study sites across China showed reasonable agreement with default values from the National Engineering Handbook (R2 = 0.76, n = 17). Among four commonly used geostatistical interpolation methods, the inverse distance weighting (IDW) method achieved the highest accuracy (R2 = 0.67, n = 209) for prediction of cropland runoff. Using default CN values and the IDW method, estimated national annual cropland runoff volume and runoff depth in 1990–2013 were 253 ± 25 km3 yr−1 and 182 ± 15 mm yr−1, respectively. Estimated cropland runoff depth gradually increased from the drier northwest inland region to the wetter southeast coastal region (range: 2–1375 mm yr−1). Regionally, eastern, central and southern China accounted for 39% of the cultivated area and 53% of the irrigated land area and contributed to 68% of the national cropland runoff volume. In contrast, northwestern, northern, southwestern and northeastern China accounted for 61% of the cultivated area and 47% of the irrigated land area and contributed to 32% of the runoff volume. Rainfall was the main source (72%) of cropland runoff for the entire nation, while irrigation became the main source of cropland runoff in drier regions (northwestern and southwestern China). Over the 24-year study period, estimated cropland runoff depth showed no significant trends, whereas cropland runoff volume and irrigation-contributed percentages decreased by 7% and 35%, respectively, owing to implementation of water-saving irrigation technologies. To reduce excessive runoff and increase water utilization efficiencies, regionally specific water management strategies should be further promoted. As the first long-term national estimate of cropland runoff in China, this study provides a simple framework for estimating regional cropland runoff depth and volume, providing critical information for guiding developments of management practices to mitigate agricultural nonpoint source pollution, soil erosion and water scarcity