A Bayesian approach to multi-source forest area estimation

In efforts such as land use change monitoring, carbon budgeting, and forecasting ecological conditions and timber supply, there is increasing demand for regional and national data layers depicting forest cover. These data layers must permit small area estimates of forest area and, most importantly, provide associated error estimates. This paper presents a model-based approach for coupling mid-resolution satellite imagery with plot-based forest inventory data to produce estimates of probability of forest and associated error at the pixel-level. The proposed Bayesian hierarchical model provides access to each pixel’s posterior predictive distribution allowing for a highly flexible analysis of pixel and multi-pixel areas of interest. The paper presents a trial using multiple dates of Landsat imagery and USDA Forest Service Forest Inventory and Analysis plot data. The results describe the spatial dependence structure within the trial site, provide pixel and multi-pixel summaries of probability of forest land use, and explore discretization schemes of the posterior predictive distributions to forest and non-forest classes. Model prediction results of a holdout set analysis suggest the proposed model provides high classification accuracy, 88%, for the trial site.

Efficient implementation of the Metropolis-Hastings algorithm,with application to the Cormack–Jolly–Seber model

Judicious choice of candidate generating distributions improves efficiency of the Metropolis-Hastings algorithm. In Bayesian applications, it is sometimes possible to identify an approximation to the target posterior distribution; this approximate posterior distribution is a good choice for candidate generation. These observations are applied to analysis of the Cormack–Jolly–Seber model and its extensions.     

Bayes methods for combining disease and exposure data in assessing environmental justice

Environmental justice reflects the equitable distribution of the burden of environmental hazards across various sociodemographic groups. The issue is important in environmental regulation, siting of hazardous waste repositories and prioritizing remediation of existing sources of exposure. We propose a statistical framework for assessing environmental justice. The framework includes a quantitative assessment of environmental equity based on the cumulative distribution of exposure within population subgroups linked to disease incidence through a dose-response function. This approach avoids arbitrary binary classifications of individuals solely as 'exposed' or 'unexposed'. We present a Bayesian inferential approach, implemented using Markov chain Monte Carlo methods, that accounts for uncertainty in both exposure and response. We illustrate our method using data on leukaemia deaths and exposure to toxic chemical releases in Allegheny County, Pennsylvania.     

An Integrated Monte Carlo Methodology for the calibration of water quality models

This paper proposes an Integrated Monte Carlo Methodology (IMCM) to solve the parameter estimation problem in water quality models. The methodology is based on Bayesian approach and Markov Chain Monte Carlo techniques and it operates by means of four modules: Markov Chain Monte Carlo (MCMC), Moving Feasible Ranges (MFR), Statistical Analysis of the Joint Posterior Distribution (SAD) and Uncertainty Propagation Analysis (UPA). The main innovation of the new proposal lies in the combination of MCMC and MFR modules which provides the joint posterior distribution of the calibrated parameters following the classical Bayesian approach. While MCMC module, based on Shuffled Complex Evolution Metropolis (SCEM-UA) algorithm, is specially designed to sample complex joint posterior shapes within certain parameter ranges, the MFR readjusts these ranges until the coverage of the feasible parameter space is guaranteed. Once the joint posterior distribution is properly defined, the SAD provides the parameter statistics and the UPA performs an analysis of the uncertainty propagation through the model. The possibilities of the new proposal have been tested on the basis of a simple model featuring different activated sludge batch experiments. IMCM has been implemented in Matlab and it is prepared to be easily connected to any software package.     

基于MLP-ANN与Markov Chain的土地利用变化预测方法——以锡林郭勒盟为例

以北方草地典型地区—内蒙古锡林郭勒盟为案例区,在1995年到2000年的土地利用变化与驱动力分析的基础上,利用土地利用转换类型和驱动力模型,采用多层感知人工神经网络模型分析了各种土地利用类型未来的转换潜力;利用马尔可夫链模型,预测了2005和2010年土地利用格局。预测结果显示：高覆盖度草地减少幅度最大,中覆盖度草地减少相对和缓,高、中覆盖度草地的减少造成了未利用地和低覆盖度草地的增加,尤其是前者增加的幅度最大;从空间分布看,高覆盖度草地的减少集中在西北部地区,主要转变为中低覆盖度草地,中覆盖度草地的减少主要集中在西南部地区,其流向主要是以沙化土地为主的未利用地;案例研究表明,多层感知人工神经网络模型与马尔可夫链模型的结合与应用能够在很大程度上预测稳定驱动力作用下的土地利用变化趋势,从而为生态干预提供指导。     

Proposing an information criterion for individual-based models developed in a pattern-oriented modelling framework

Individual-based models (IBMs) have been improved in quality and reliability in recent years with an approach called pattern-oriented modelling (POM). POM proposes guidelines to develop models reproducing multiple patterns observed on the field and to test systematically how well the IBMs reproduce them. POM studies used generally traditional methods of goodness of fit such as the sum of squares evaluation or ad hoc comparisons of fitting errors and variations. Model selection, however, can be a rigorous statistical approach based on information theory and information criteria such as the Akaike's information criterion (AIC) or the deviance information criterion (DIC). So far, it has not been tried to link POM to these rigorous techniques. The main problems to achieve that are: (a) the difficulty to have likelihood functions for IBMs’ parameters and (b) the possibility to obtain posterior distributions of IBMs’ parameters given the patterns to reproduce. In a first part, this paper answers problem (a) by proposing and explaining how to calculate a deviance measure (POMDEV) for models developed in a context of POM. And while answering the second problem, a second part of the paper proposes an information criterion for model selection in a POM context (the pattern-oriented modelling information criterion: POMIC). This criterion does not yet have the same theoretical foundation as, e.g., AIC, but uses formal analogies to the DIC. In a third part POMIC is tested with a modelling exercise. This exercise shows the potential of POMIC to use multiple patterns for selecting among multiple potential submodels and eventually select the most parsimonious and well fitting model version. We conclude that POMIC, although being a heuristically derived approach, can greatly improve the POM framework.     

Performance of a Bayesian state-space model of semelparous species for stock-recruitment data subject to measurement error

Measurement errors in spawner abundance create problems for fish stock assessment scientists. To deal with measurement error, we develop a Bayesian state-space model for stock-recruitment data that contain measurement error in spawner abundance, process error in recruitment, and time series bias. Through extensive simulations across numerous scenarios, we compare the statistical performance of the Bayesian state-space model with that of standard regression for a traditional stock-recruitment model that only considers process error. Performance varies depending on the information content in data, as determined by stock productivity, types of harvest situations, and amount of measurement error. Overall, in terms of estimating optimal spawner abundance S_MSY, the Ricker density-dependence parameter β, and optimal harvest rate h_MSY, the Bayesian state-space model works best for informative data from low and variable harvest rate situations for high-productivity salmon stocks. The traditional stock-recruitment model (TSR) may be used for estimating α and h_MSY for low-productivity stocks from variable and high harvest rate situations. However, TSR can severely overestimate S_MSY when spawner abundance is measured with large error in low and variable harvest rate situations. We also found that there is substantial merit in using h_MSY (or benchmarks derived from it) instead of S_MSY as a management target.     

On the latent state estimation of nonlinear population dynamics using Bayesian and non-Bayesian state-space models

Nonlinear state-space models have been increasingly applied to study population dynamics and data assimilation in environmental sciences. State-space models can account for process error and measurement error simultaneously to correct for the bias in the estimates of system state and model parameters. However, few studies have compared the performance of different nonlinear state-space models for reconstructing the state of population dynamics from noisy time series. This study compared the performance of the extended Kalman filter (EKF), unscented Kalman filter (UKF) and Bayesian nonlinear state-space models (BNSSM) through simulations. Synthetic population time series were generated using the theta logistic model with known parameters, and normally distributed process and measurement errors were introduced using the Monte Carlo simulations. At higher levels of nonlinearity, the UKF and BNSSM had lower root mean square error (RMSE) than the EKF. The BNSSM performed reliably across all levels of nonlinearity, whereas increased levels of nonlinearity resulted in higher RMSE of the EKF. The Metropolis–Hastings algorithm within the Gibbs algorithm was used to fit the theta logistic model to synthetic time series to estimate model parameters. The estimated posterior distribution of the parameter θ indicated that the 95% credible intervals included the true values of θ (=0.5 and 1.5), but did not include 1.0 and 0.0. Future studies need to incorporate the adaptive Metropolis algorithm to estimate unknown model parameters for broad applications of Bayesian nonlinear state-space models in ecological studies.     

A Bayesian hierarchical model for monitoring harbor seal changes in Prince William Sound, Alaska

Bayesian hierarchical models were used to assess trends of harbor seals, Phoca vitulina richardsi, in Prince William Sound, Alaska, following the 1989 Exxon Valdez oil spill. Data consisted of 4–10 replicate observations per year at 25 sites over 10 years. We had multiple objectives, including estimating the effects of covariates on seal counts, and estimating trend and abundance, both per site and overall. We considered a Bayesian hierarchical model to meet our objectives. The model consists of a Poisson regression model for each site. For each observation the logarithm of the mean of the Poisson distribution was a linear model with the following factors: (1) intercept for each site and year, (2) time of year, (3) time of day, (4) time relative to low tide, and (5) tide height. The intercept for each site was then given a linear trend model for year. As part of the hierarchical model, parameters for each site were given a prior distribution to summarize overall effects. Results showed that at most sites, (1) trend is down; counts decreased yearly, (2) counts decrease throughout August, (3) counts decrease throughout the day, (4) counts are at a maximum very near to low tide, and (5) counts decrease as the height of the low tide increases; however, there was considerable variation among sites. To get overall trend we used a weighted average of the trend at each site, where the weights depended on the overall abundance of a site. Results indicate a 3.3% decrease per year over the time period.     

Nutrient criteria for lakes,ponds, and reservoirs: A Bayesian TREED model approach

We develop regional-scale eutrophication models for lakes, ponds, and reservoirs to investigate the link between nutrients and chlorophyll-a. The Bayesian TREED (BTREED) model approach allows association of multiple environmental stressors with biological responses, and quantification of uncertainty sources in the empirical water quality model. Nutrient data for lakes, ponds, and reservoirs across the United States were obtained from the Environmental Protection Agency (EPA) National Nutrient Criteria Database. The nutrient data consist of measurements for both stressor variables (such as total nitrogen and total phosphorus), and response variables (such as chlorophyll-a), used in the BTREED model. Markov chain Monte Carlo (McMC) posterior exploration guides a stochastic search through a rich suite of candidate trees toward models that better fit the data. The Bayes factor provides a goodness of fit criterion for comparison of resultant models. We randomly split the data into training and test sets; the training data were used in model estimation, and the test data were used to evaluate out-of-sample predictive performance of the model. An average relative efficiency of 1.02 between the training and test data for the four highest log-likelihood models suggests good out-of-sample predictive performance. Reduced model uncertainty relative to over-parameterized alternative models makes the BTREED models useful for nutrient criteria development, providing the link between nutrient stressors and meaningful eutrophication response.     

An integrated optimization and simulation approach for air pollution control under uncertainty in open-pit metal mine

Air Pollution Control model is developed for open-pit metal mines. Model will aid decision makers to select a cost-effective solution. Open-pit metal mines contribute toward air pollution and without effective control techniques manifests the risk of violation of environmental guidelines. This paper establishes a stochastic approach to conceptualize the air pollution control model to attain a sustainable solution. The model is formulated for decision makers to select the least costly treatment method using linear programming with a defined objective function and multi-constraints. Furthermore, an integrated fuzzy based risk assessment approach is applied to examine uncertainties and evaluate an ambient air quality systematically. The applicability of the optimized model is explored through an open-pit metal mine case study, in North America. This method also incorporates the meteorological data as input to accommodate the local conditions. The uncertainties in the inputs, and predicted concentration are accomplished by probabilistic analysis using Monte Carlo simulation method. The output results are obtained to select the cost-effective pollution control technologies for PM_2.5, PM₁₀, NO_x, SO₂ and greenhouse gases. The risk level is divided into three types (loose, medium and strict) using a triangular fuzzy membership approach based on different environmental guidelines. Fuzzy logic is then used to identify environmental risk through stochastic simulated cumulative distribution functions of pollutant concentration. Thus, an integrated modeling approach can be used as a decision tool for decision makers to select the cost-effective technology to control air pollution.     

Assessing and testing prediction uncertainty for single tree-based models: A case study applied to northern hardwood stands in southern Québec, Canada

Estimating prediction uncertainty for a single tree-based model is hindered by the complex structure of these models. In this paper, we addressed this issue with a case study applied to northern hardwood stands in Québec, Canada. SaMARE is a stochastic single tree-based model that was designed for these types of stands. Using a Monte Carlo approach, the model can provide a mean predicted value and its confidence limits for some plot-level attributes.The mean predicted values were compared to observed values in terms of bias and accuracy. In addition to these common statistics, we compared nominal coverage of Monte Carlo-simulated confidence intervals with real (observed) coverage to verify the adequacy of the simulated uncertainty. A comparison was made using several plot-level attributes, which exhibited an increasing discriminative complexity. This complexity ranges from coarse attributes, such as all-species basal area, up to more complex ones, such as basal area for stems of a particular species and with sawlog potential.The results showed that in terms of absolute value, biases were small, but could be relatively high with respect to the average observed value when the discriminative complexity of the attribute increased. The comparison between nominal and real coverage of confidence intervals gave satisfactory results for all-species plot-level attributes. However, for some species-specific attributes, the Monte Carlo-simulated confidence intervals overestimated the real coverage.     

A novel hybrid model for water quality prediction based on VMD and IGOA optimized for LSTM

● A novel VMD-IGOA-LSTM model has proposed for the prediction of water quality. ● Improved model quickly converges to the global optimal fitness and remains stable. ● The prediction accuracy of water quality parameters is significantly improved. Water quality prediction is vital for solving water pollution and protecting the water environment. In terms of the characteristics of nonlinearity, instability, and randomness of water quality parameters, a short-term water quality prediction model was proposed based on variational mode decomposition (VMD) and improved grasshopper optimization algorithm (IGOA), so as to optimize long short-term memory neural network (LSTM). First, VMD was adopted to decompose the water quality data into a series of relatively stable components, with the aim to reduce the instability of the original data and increase the predictability, then each component was input into the IGOA-LSTM model for prediction. Finally, each component was added to obtain the predicted values. In this study, the monitoring data from Dayangzhou Station and Shengmi Station of the Ganjiang River was used for training and prediction. The experimental results showed that the prediction accuracy of the VMD-IGOA-LSTM model proposed was higher than that of the integrated model of Ensemble Empirical Mode Decomposition (EEMD), the integrated model of Complete Ensemble Empirical Mode Decomposition with Adaptive Noise (CEEMDAN), Nonlinear Autoregressive Network with Exogenous Inputs (NARX), Recurrent Neural Network (RNN), as well as other models, showing better performance in short-term prediction. The current study will provide a reliable solution for water quality prediction studies in other areas.     

A general model for tagging on multiple component fisheries: an integration of age-dependent reporting rates and mortality estimation

A major objective of analyzing multiple year tag return data in fisheries is to estimate fishing and natural mortality rates which may vary by age class and calendar year. To do this one needs to be able to estimate the reporting rates for the tags recovered. Some fisheries such as that for Southern Bluefin Tuna (Thunnus maccoyii) have multiple components with potentially different reporting rates for the tag returns. In this paper we develop a general model for multi-cohort, multi-year tag return analyses where there are multiple components to the fishery with potentially different reporting rates. We require the assumption that one component has a reporting rate of 100% (i.e., this could be the component of a boat based fishery where scientific observers are present). We show further how it is possible to partition the overall likelihood developed into two conditionally independent components. The first component of the likelihood is the standard multinomial likelihood that allows estimation of fishing and natural mortality rates. It uses the tag return matrix summed over all the components of the fishery. It requires an average reporting rate for the tag returns (where the average reporting rate is a weighted average of the individual reporting rates of the different components). The second component is also multinomial for the individual component tag returns and allows us to estimate individual component reporting rates. However, this requires that we augment our second component tag return likelihood with a catch data likelihood for the corresponding components. The methodology is illustrated on some Southern Bluefin Tuna tagging and catch data. We also discuss important model assumptions and give suggestions for future research including the integration of tag-return and catch at age data analyses.     

A geostatistical approach for mapping thematic classification accuracy and evaluating the impact of inaccurate spatial data on ecological model predictions

Spatial information in the form of geographical information system coverages and remotely sensed imagery is increasingly used in ecological modeling. Examples include maps of land cover type from which ecologically relevant properties, such as biomass or leaf area index, are derived. Spatial information, however, is not error-free: acquisition and processing errors, as well as the complexity of the physical processes involved, make remotely sensed data imperfect measurements of ecological attributes. It is therefore important to first assess the accuracy of the spatial information being used and then evaluate the impact of such inaccurate information on ecological model predictions. In this paper, the role of geostatistics for mapping thematic classification accuracy through integration of abundant image-derived (soft) and sparse higher accuracy (hard) class labels is presented. Such assessment leads to local indices of map quality, which can be used for guiding additional ground surveys. Stochastic simulation is proposed for generating multiple alternative realizations (maps) of the spatial distribution of the higher accuracy class labels over the study area. All simulated realizations are consistent with the available pieces of information (hard and soft labels) up to their validated level of accuracy. The simulated alternative class label representations can be used for assessing joint spatial accuracy, i.e., classification accuracy regarding entire spatial features read from the thematic map. Such realizations can also serve as input parameters to spatially explicit ecological models; the resulting distribution of ecological responses provides a model of uncertainty regarding the ecological model prediction. A case study illustrates the generation of alternative land cover maps for a Landsat Thematic Mapper (TM) subscene, and the subsequent construction of local map quality indices. Simulated land cover maps are then input into a biogeochemical model for assessing uncertainty regarding net primary production (NPP).     

Population dynamics models based on cumulative density dependent feedback: A link to the logistic growth curve and a test for symmetry using aphid data

Density dependent feedback, based on cumulative population size, has been advocated to explain and mathematically characterize “boom and bust” population dynamics. Such feedback results in a bell-shaped population trajectory of the population density. Here, we note that this trajectory is mathematically described by the logistic probability density function. Consequently, the cumulative population follows a time trajectory that has the same shape as the cumulative logistic function. Thus, the Pearl–Verhulst logistic equation, widely used as a phenomenological model for density dependent population growth, can be interpreted as a model for cumulative rather than instantaneous population. We extend the cumulative density dependent differential equation model to allow skew in the bell-shaped population trajectory and present a simple statistical test for skewness. Model properties are exemplified by fitting population trajectories of the soybean aphid, Aphis glycines. The linkage between the mechanistic underpinnings of the logistic probability density function and cumulative distribution function models could open up new avenues for analyzing population data.