基于ARIMA模型的湘江流域DO和NH4+–N含量贝叶斯预测

为实时把控湘江流域水质的变化趋势,采用污染比较严重的湘江流域长沙段和益阳段水质指标溶解氧(DO)和氨氮(NH_4~+-N)含量的监测数据,用贝叶斯方法推断经典的ARIMA时间序列模型,并用马尔可夫链蒙特卡罗(MCMC)模拟方法对DO和NH_4~+-N含量进行贝叶斯预测。结果表明,该模型的贝叶斯预测能实现对湘江流域长沙段和益阳段水质指标DO和NH_4~+-N含量的精确点预测、区间预测和概率预测。     

Temporal associations between low body condition,lameness and milk yield in a UK dairy herd

Previous work has hypothesised that cows in low body condition become lame. We tested this in a prospective longitudinal study. Body condition score (BCS), causes of lameness and milk yield were collected from a 600-cow herd over 44-months. Mixed effect binomial models and a continuous outcome model were used to investigate the associations between lameness, BCS and milk yield. In total, 14,320 risk periods were obtained from 1137 cows. There were 1510 lameness treatments: the most common causes of lameness were sole ulcer (SU) (39%), sole haemorrhage (SH) (13%), digital dermatitis (DD) (10%) and white line disease (WLD) (8%). These varied by year and year quarter. Body condition was scored at 60-day intervals. BCS ranged from 1 to 5 with a mean of 2.5, scores were higher in very early lactation but varied widely throughout lactation; approximately 45% of scores were <2.5. The key finding was that BCS < 2.5 was associated with an increased risk of treatment for lameness in the following 0–2 months and >2–4 months for all causes of lameness and also specifically for SU/WLD lameness. BCS < 2.5 was associated with an increased risk of treatment for SH in the following 0–2 months but not >2–4 months. There was no such association with DD. All lameness, SU/WLD, SH and DD were significantly more likely to occur in cows that had been lame previously, but the effect of BCS was present even when all repeat cases of lameness were excluded from the analysis. Milk yield was significantly higher and fell in the month before treatment in cows lame with SU/WLD but it was not significantly higher for cows that were treated for DD compared with non-lame cows. These findings support the hypothesis that low BCS contributes to the development of horn related claw lameness but not infectious claw diseases in dairy cows. One link between low BCS and lameness is a thin digital cushion which has been proposed as a trigger for claw horn disease. Cows with BCS 2 produced more milk than cows with BCS 2.5, however, this was only approximately 100 kg difference in yield over a 305-day lactation. Given the increased risk of lameness in cows with BCS 2, the direct costs of lameness and the small variability in milk yield by BCS, preventing cows from falling to BCS < 2.5 would improve cow welfare and be economically beneficial.     

Predicting the rate of range expansion of an invasive alien bumblebee (Bombus terrestris) using a stochastic spatio-temporal model

To develop effective strategies for managing biological invasions, it is important to understand and be able to predict patterns of invasion and range expansion, and particularly the rate of spread and factors controlling this rate. To predict the spatial dynamics of invasion by an alien bumblebee (Bombus terrestris) in Hokkaido, Japan, we explicitly constructed a stochastic spatio-temporal model that incorporates immigration and establishment processes. Using a Bayesian approach, we parameterized the model based on spatio-temporal presence/absence data collected by citizen volunteers and used the model to predict control of the near-future spread of the bumblebee under several management strategies. The range expansion dynamics of B. terrestris were significantly negatively affected by two aspects of environmental heterogeneity: the land-use pattern (the proportion of woodland) and climate (the snow depth). Of the several spatial management strategies, suppressing the outlying (edge) colonies would be the most efficient strategy to reduce the bumblebee’s spread, irrespective of the level of effort, and would significantly slow the bumblebee’s range expansion during the next 30 years. The modeling approach employed in the present study will be broadly useful for studying real-world biological invasion problems, for which prediction of the progress of an invasion, even in the very near future, is urgently needed to support effective spatial management options and countermeasures. In addition, the model demonstrates that incorporating the dynamics of environmental heterogeneity is a fundamental requirement for prediction and risk assessment during biological invasions, especially in the context of recent rapid changes in the environment at regional and global scales.     

境外对公职人员收受礼品行为的规制及其启示

鉴于美式期权的定价具有后向迭代搜索特征,本文结合Longstaff和Schwartz提出的美式期权定价的最小二乘模拟方法,研究基于马尔科夫链蒙特卡洛算法对回归方程系数的估计,实现对美式期权的双重模拟定价.通过对无红利美式看跌股票期权定价进行大量实证模拟,从期权价值定价误差等方面同著名的最小二乘蒙特卡洛模拟方法进行对比分析,结果表明基于MCMC回归算法给出的美式期权定价具有更高的精确度.模拟实证结果表明本文提出的对美式期权定价方法具有较好的可行性、有效性与广泛的适用性.该方法的不足之处就是类似于一般的蒙特卡洛方法,会使得求解的计算量有所加大.     

基于改进粒子滤波的农用车辆导航定位方法

针对农业机械导航系统中常用的Kalman滤波对多传感器数据进行融合的算法不适用于非线性农用车辆导航系统的问题,该文采用粒子滤波方法进行数据融合,以获得准确的导航定位信息;该算法增加抗野值步骤,有效削弱GPS跳变引起的误差;通过对重要密度函数进行改进,引入无迹卡尔曼滤波方法（UKF）,并采用不同重采样方法,有效抑制了粒子退化;增加MCMC步骤,减少了样本枯竭现象。仿真结果表明,改进后粒子滤波方法,可有效提高精度,减小导航误差,可满足农用车辆与作业机械的导航要求。     

谷物胚乳性状QTL区间作图的贝叶斯方法

将贝叶斯统计原理和胚乳性状的数量遗传模型相结合,以分离群体中各植株的分子标记基因型以及植株上若干粒种子胚乳性状的单粒观测值为数据模式,提出胚乳性状QTL区间作图的贝叶斯方法.该方法通过Gibbs以及Metropolis-Hastings抽样实现的马尔科夫链蒙特卡罗(MCMC)算法获得QTL效应和位置的估计.方法的有效性用染色体水平和基因组水平2套模拟方案进行验证,结果表明:贝叶斯方法能够准确地估计胚乳性状QTL的位置和效应,并同时区分2种显性效应.     

Assessing the convergence of Markov Chain Monte Carlo methods: an example from evaluation of diagnostic tests in absence of a gold standard

The accessibility of Markov Chain Monte Carlo (MCMC) methods for statistical inference have improved with the advent of general purpose software. This enables researchers with limited statistical skills to perform Bayesian analysis. Using MCMC sampling to do statistical inference requires convergence of the MCMC chain to its stationary distribution. There is no certain way to prove convergence; it is only possible to ascertain when convergence definitely has not been achieved. These methods are rather subjective and not implemented as automatic safeguards in general MCMC software. This paper considers a pragmatic approach towards assessing the convergence of MCMC methods illustrated by a Bayesian analysis of the Hui–Walter model for evaluating diagnostic tests in the absence of a gold standard. The Hui–Walter model has two optimal solutions, a property which causes problems with convergence when the solutions are sufficiently close in the parameter space. Using simulated data we demonstrate tools to assess the convergence and mixing of MCMC chains using examples with and without convergence. Suggestions to remedy the situation when the MCMC sampler fails to converge are given. The epidemiological implications of the two solutions of the Hui–Walter model are discussed.     

Measuring soil disturbance effects and assessing soil restoration success by examining distributions of soil properties

Successful restoration of an ecosystem following disturbance is typically assessed according to similarity between the restored site and a relatively undisturbed reference area. While most comparisons use the average or mean parameter to represent measured properties, other aspects of the distribution, including the variance of the properties may assist in a more robust assessment of site recovery. Our purpose was to compare soil properties in different ages of reclaimed soils with those in reference areas by incorporating the potentially different distributions according to areas. On two sampling dates, in consecutive years, we examined soil properties on a chronosequence of reclaimed natural gas pipelines spanning recovery ages of <1–54 years, obtaining data on soil moisture, organic carbon, nitrogen, electrical conductivity, pH, and microbial abundance. To make the comparisons, we analyzed our data with a Bayesian hierarchical linear mixed model and obtained posterior predictive distributions for the soil properties. This allowed us to probabilistically quantify the extent to which a soil property from a reclaimed treatment was similar to that from an undisturbed reference. We found that the posterior predictive variance of most soil properties was particularly sensitive to disturbance and reclamation, especially, within the first few years of recovery. Response of this variance to disturbance, reclamation, and recovery was not necessarily accompanied by a shift in the posterior predictive mean value of the property. Patterns for all soil properties changed over time, with posterior predictive distributions of soil properties generally becoming more similar to those of the undisturbed reference sites as recovery time increased. We suspect these trends in altered variability coincide with the degree of spatial heterogeneity in soil properties that results following disturbance and reclamation, which is also coupled to patterns of vegetation recovery.     

基于先验知识的MCMC在混合像元分解中的应用研究

MCMC方法是一种动态的参数估计方法,研究MCMC方法在遥感影像混合像元分解中的应用。传统的混合像元分解一般是基于固定端元的,而实际上影像中像元并不都是由完全相同的端元组成。基于MCMC方法提出了一种端元可变的像元分解算法,并且充分利用了端元的累计先验知识。算法将端元选取和丰度反演合为一个步骤,抽象成一个估计参数的随机过程,在端元数目可变的前提下,基于可逆的跳跃式MCMC方法估计参数。在状态转移过程中,加入端元的累计先验知识,提高算法效率。这种算法不需要人工干预,能够实现自动化像元分解,并且具有较高的精度。结果表明,基于修正MCMC的端元可变的自动化解混算法在分解精度和稳定性方面均优于基于固定端元的混合像元分解方法。     

Reliable computing in estimation of variance components

The purpose of this study is to present guidelines in selection of statistical and computing algorithms for variance components estimation when computing involves software packages. For this purpose two major methods are to be considered: residual maximal likelihood (REML) and Bayesian via Gibbs sampling. Expectation‐Maximization (EM) REML is regarded as a very stable algorithm that is able to converge when covariance matrices are close to singular, however it is slow. However, convergence problems can occur with random regression models, especially if the starting values are much lower than those at convergence. Average Information (AI) REML is much faster for common problems but it relies on heuristics for convergence, and it may be very slow or even diverge for complex models. REML algorithms for general models become unstable with larger number of traits. REML by canonical transformation is stable in such cases but can support only a limited class of models. In general, REML algorithms are difficult to program. Bayesian methods via Gibbs sampling are much easier to program than REML, especially for complex models, and they can support much larger datasets; however, the termination criterion can be hard to determine, and the quality of estimates depends on a number of details. Computing speed varies with computing optimizations, with which some large data sets and complex models can be supported in a reasonable time; however, optimizations increase complexity of programming and restrict the types of models applicable. Several examples from past research are discussed to illustrate the fact that different problems required different methods.