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 strategy for combining predictions from empirical and process-based models

We present a strategy for using an empirical forest growth model to reduce uncertainty in predictions made with a physiological process-based forest ecosystem model. The uncertainty reduction is carried out via Bayesian melding, in which information from prior knowledge and a deterministic computer model is conditioned on a likelihood function. We used predictions from an empirical forest growth model G-HAT in place of field observations of aboveground net primary productivity (ANPP) in a deciduous temperate forest ecosystem. Using Bayesian melding, priors for the inputs of the process-based forest ecosystem PnET-II were propagated through the model, and likelihoods for the PnET-II output ANPP were calculated using the G-HAT predictions. Posterior distributions for ANPP and many PnET-II inputs obtained using the G-HAT predictions largely matched posteriors obtained using field data. Since empirical growth models are often more readily available than extensive field data sets, the method represents a potential gain in efficiency for reducing the uncertainty of process-based model predictions when reliable empirical models are available but high-quality data are not.     

Active Adaptive Management for Conservation

Abstract:  Active adaptive management balances the requirements of management with the need to learn about the system being managed, which leads to better decisions. It is difficult to judge the benefit of management actions that accelerate information gain, relative to the benefit of making the best management decision given what is known at the time. We present a first step in developing methods to optimize management decisions that incorporate both uncertainty and learning via adaptive management. We assumed a manager can allocate effort to discrete units (e.g., areas for revegetation or animals for reintroduction), the outcome can be measured as success or failure (e.g., the revegetation in an area is successful or the animal survives and breeds), and the manager has two possible management options from which to choose. We further assumed that there is an annual budget that may be allocated to one or both of the two options and that the manager must decide on the allocation. We used Bayesian updating of the probability of success of the two options and stochastic dynamic programming to determine the optimal strategy over a specified number of years. The costs, level of certainty about the success of the two options, and the timeframe of management all influenced the optimal allocation of the annual budget. In addition, the choice of management objective had a large influence on the optimal decision. In a case study of Merri Creek, Melbourne, Australia, we applied the approach to determining revegetation strategies. Our approach can be used to determine how best to manage ecological systems in the face of uncertainty.     

Neighborhood Level Spatial Analysis of the Relationship Between Alcohol Outlet Density and Criminal Violence

Misuse of alcohol is a significant public health problem, potentially resulting in unintentional injuries, motor vehicle crashes, drownings, and, perhaps of greatest concern, serious acts of violence, including assaults, rapes, suicides, and homicides. Although previous research establishes a link between alcohol consumption increased levels of violence, studies relating the density of alcohol outlets (e.g., restaurants, bars, liquor stores) and the likelihood of violent crime have been less common. In this paper we test for such a relationship at the small area level, using data from 79 neighborhoods in the city of Minneapolis, Minnesota. We adopt a fully Bayesian point of view using Markov chain Monte Carlo (MCMC) computational methods as available in the popular and freely available WinBUGS language. Our models control for important covariates (e.g., neighborhood racial heterogeneity, age heterogeneity) and also account for spatial association in unexplained variability using conditionally autoregressive (CAR) random effects. Our results indicate a significant positive relationship between alcohol outlet density and violent crime, while also permitting easy mapping of neighborhood-level predicted and residual values, the former useful for intervention in the most at-risk neighborhoods and the latter potentially useful in identifying covariates still missing from the fixed effects portion of the model.     

The ‘Bayesics’ of Ranked Set Sampling

Ranked set sampling can be useful when measurements are expensive but units from the popu- lation can be easily ranked. In this situation one may draw k units from the population, rank them, select one on which to make the expensive measurement, draw another k units, rank them, select one, and so on. The method was originally suggested by McIntyre (1952) in connection with pasture yields and is obviously applicable in other situations as well. Dell and Clutter (1972) and Patil et al. (1994) explain the basics from a classical point of view. Our aim is to examine the procedure from a Bayesian point of view, determine whether ranked set sampling provides advantages over simple random sampling and explore some optimality questions     

车装焊复合加工装备的服役可靠性评估

目的评估某型航天用车装焊复合加工装备在服役过程中的服役可靠性。方法首先分析装备常见的故障模式,统计装备在使用过程中的故障数据,由于装备故障数据样本量较少,所以提出基于贝叶斯理论的小样本车装焊复合加工装备可靠性评估方法,其中通过马尔科夫链蒙特卡罗(MCMC)法抽样解决贝叶斯理论中后验积分复杂的问题。结果确定了车装焊复合加工装备的寿命威布尔分布模型,并运用贝叶斯方法,计算出该车装焊复合加工装备的平均无故障工作时间(MTBF)。结论评估结果略低于设计要求,原因是目前该装备处于服役初期,服役初期故障数据较多。待进入稳定服役期时,故障率会有一定程度的降低后趋于稳定,MTBF会有一定幅度的增加,所以该车装焊复合加工装备MTBF基本满足设计要求。     

基于BN的FTA在通用航空风险评价中的应用

针对事故树分析法(FTA)在风险评价中的局限性,采用以事故树为基础建立的贝叶斯网络(BN)风险模型,对通用航空中的两机空中相撞事故进行分析和推理,对事故模型进行改进和修正时,注重基事件的多态性和事件间的逻辑合理性。根据贝叶斯推理得出的数据,找到了事故的主要致因。结果表明,基于BN的FTA既能向前预测顶事件的发生概率,又能向后诊断基本事件的后验概率,可以更好地对通用航空风险进行评价。     

基于贝叶斯网络的航空器看错落错跑道事件研究

目前,航空器看错、落错跑道事件在国际上是一个相当突出的安全问题,这个问题在我国近年也突显出来。导致航空器看错落错跑道的原因十分复杂,且此类事件及易引发严重的后果,造成人、财、物等多方面的损失,本文特对此类问题开展了一系列的研究。为了预防航空器看错、落错跑道事故的发生,查找诱发该类事故的因素,针对航空器看错、落错跑道事故的形成特点,笔者运用贝叶斯网络探讨其各影响因素间的关系和相互作用,该网络强大的逻辑推理能力,克服了不完备样本空间带来的不足,揭示了人、机、环境与管理因素相互作用的内在规律。为改善机场安全管理的科学性、可靠性,进一步降低事故率,提供了可靠的技术支持。     

基于贝叶斯网络的基本农田划定方法

基本农田划定是落实耕地保护、保证粮食安全的关键问题。目前,基本农田划定的相关研究多基于对耕地适宜性条件的评价,而未涉及对耕地历史变化过程的考虑,因而不能保证划定结果适应实际区域的耕地变化趋势,导致基本农田易被占用,补划与调整频繁。论文综合考虑耕地适宜性条件与历史动态变化状况,提出了一种基于贝叶斯网络模型的基本农田划定方法。以湖北省大冶市这一典型资源型城市为实验区进行了实例研究,划定结果表明,该划定方法能在保证基本农田划定数量与质量的同时,提高其农业用途的稳定性,促进基本农田保护与经济建设、生态保护间协调发展,是一种有效的划定模型。     

Simulation of long-term nutrient removal in a full-scale closed-loop bioreactor for sewage treatment: an example of Bayesian inference

In this study, the performance of nitrogen and phosphorus removal in a full-scale closed-loop bioreactor (oxidation ditch) system was simulated using the ASM2d model. Routine data describing the process for two years were compiled for calibration and validation. To overcome the identifiability problem, the classic Bayesian inference approach was utilized for parameter estimation. The calibrated model could describe the long-term trend of nutrient removal and short-term variations of the process performance, showing that the Bayesian method was a reliable and useful tool for the parameter estimation of the activated sludge models. The anoxic phosphate uptake by polyphosphate accumulating organisms (PAO) contributed 71.2% of the total Poly-P storage, which reveals the dominance of denitrifying phosphorus removal process under the oxygen limiting conditions. It was found that 58.7% of the anoxic Poly-P storage and denitrification by PAO in the reactor was achieved in the aerated compartment, implying that the PAO’s anoxic activity was significantly stimulated by the low dissolved oxygen (DO) level in this compartment due to the oxygen gradient caused by brush aerator.