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.     

Adaptive two-stage one-per-stratum sampling

We briefly describe adaptive cluster sampling designs in which the initial sample is taken according to a Markov chain one-per-stratum design (Breidt, 1995) and one or more secondary samples are taken within strata if units in the initial sample satisfy a given condition C. An empirical study of the behavior of the estimation procedure is conducted for three small artificial populations for which adaptive sampling is appropriate. The specific sampling strategy used in the empirical study was a single random-start systematic sample with predefined systematic samples within strata when the initially sampled unit in that stratum satisfies C. The bias of the Horvitz-Thompson estimator for this design is usually very small when adaptive sampling is conducted in a population for which it is suited. In addition, we compare the behavior of several alternative estimators of the standard error of the Horvitz-Thompson estimator of the population total. The best estimator of the standard error is population-dependent but it is not unreasonable to use the Horvitz-Thompson estimator of the variance. Unfortunately, the distribution of the estimator is highly skewed hence the usual approach of constructing confidence intervals assuming normality cannot be used here.     

基于等维新息灰色马尔科夫的地铁客流量预测*

为准确预测地铁客流量的发展趋势,采用等维新息灰色GM（1,1）预测模型与马尔科夫模型相结合的方式建立等维新息灰色马尔科夫模型,探讨等维新息灰色马尔科夫模型在地铁客流量预测领域的应用;运用平均相对误差、后验差比值和小误差概率3种指标对模型精度进行检验。结果表明:等维新息灰色马尔科夫模型与原始数列的拟合程度较高,预测精度等级为Ⅰ级（优）,优于传统灰色GM(1,1)模型和等维新息灰色GM(1,1)模型的预测精度,更加符合地铁客流的实际情况。     

Modelling Replicated Weed Growth Data using Spatially-varying Growth Curves

Weed growth in agricultural fields constitutes a major deterrent to the growth of crops, often resulting in low productivity and huge losses for the farmers. Therefore, proper understanding of patterns in weed growth is vital to agricultural research. Recent advances in Geographical Information Systems (GIS) now allow geocoding of agricultural data, which enable more sophisticated spatial analysis. Our current application concerns the development of statistical models for conducting spatial analysis of growth patterns in weeds. Our data comes from an experiment conducted in Waseca, Minnesota, that recorded growth of the weed Setariaspp. We capture the spatial variation in Setaria spp. growth using spatially-varying growth curves. An added challenge is that these designs are spatially replicated, with each plot being a lattice of sub-plots. Therefore, spatial variation may exist at different resolutions – a macro level variation between the plots and micro level variation between the sub-plots nested within each plot. We develop a Bayesian hierarchical framework for this setting. Flexible classes of models result which are fitted using simulation-based methods.     

基于灰色-马尔可夫藕合模型的区域建设用地需求预测

建设用地需求的中长期准确预测是当前土地资源规划和利用的重点和难点。本文将灰色和马尔可夫两种预测模型相结合,建立灰色-马尔可夫藕合模型,以广东省揭阳市为例,对1997到2010年间主要建设用地规模进行了需求预测,同时与其它几种常规的预测方法进行了比较。结果表明,人文驱动力相关预测法误差相对较大,其中国内生产总值(GDP)相关法准确度要优于人口相关法。趋势线法计算简单,预测准确度也相对较高,但只适于短期预测。灰色预测法精确度较高,计算需要模型的支持、专业性强。灰色-马尔可夫预测法由于是对灰色预测的偏离值进行了纠正,因而准确度最高。尽管该方法需要大量数据的支持,计算量大,但仍是值得推荐的高准确度的区域建设用地的专业预测方法。     

供应链系统可靠性分析

供应链是由物料获取并加工成中间件或成品 ,再将成品送到顾客手中的一些企业和部门构成的网络 ,它包括供应商 (包括供应商的供应商等 )、制造商、配送中心、零售商、最终用户等多个多级实体。除了性能以外 ,其可靠性已经成为供应链管理研究的重点。鉴于供应链中存在的诸多层次与环节致使供应链的可靠性分析十分复杂 ,为了简便起见 ,笔者认为 ,必须从单级供应链可靠性分析出发 ,再进行基于马尔可夫过程的多级供应链可靠性分析 ,最后根据分析结果 ,提出一些提高供应链可靠性的措施。该方法对供应链系统可靠性分析具有实用价值 ,其关键环节是将串联结构改变为并联结构来实现。     

马尔柯夫预测模型在环境预测中的应用

马尔柯夫预测模型利用系统的现在状态和发展方向去预测系统将来可能状态的概率。它在选择污染治理策略，环境状态变化的可能方向及发展趋势预测等方面地产可应用，其预测结果为某事件实现的概率即可能程度。     

Bayesian Nonstationary Frequency Analysis of Hydrological Variables1

Ouarda, T.B.M.J. and S. El‐Adlouni, 2011. Bayesian Nonstationary Frequency Analysis of Hydrological Variables. Journal of the American Water Resources Association (JAWRA) 47(3):496‐505. DOI: 10.1111/j.1752‐1688.2011.00544.x Abstract: The present paper provides a discussion of nonstationary frequency analysis models in hydrology with a focus on the Bayesian approach. The Bayesian model provides an efficient estimation framework of hydrological quantiles in the presence of nonstationarity. In nonstationary frequency analysis models, the parameters are functions of covariates, allowing for dependent parameters and trends. The use of the nonstationary Generalized Maximum Likelihood Estimation method in hydrologic frequency analysis is discussed. This model allows using prior information concerning the variables under study and considering a number of models (linear, quadratic, etc.) of the dependence of the parameters on covariates. A discussion is also provided concerning the use of the reversible jump Monte Carlo Markov Chain procedure which allows carrying out the estimation of the posterior distributions of the parameters and the selection of the Bayesian model at the same time. An application to a case study is presented to illustrate the potential of the model.     

Modeling fecundity in birds: Conceptual overview, current models, and considerations for future developments

Fecundity is fundamental to the fitness, population dynamics, conservation, and management of birds. For all the efforts made to measure fecundity or its surrogates over the past century of avian research, it is still mismeasured, misrepresented, and misunderstood. Fundamentally, these problems arise because of partial observability of underlying processes such as renesting, multiple brooding, and temporary emigration. Over the last several decades, various analytical approaches have been developed to estimate fecundity from incomplete and biased data. These, include scalar arithmetic formulae, partial differential equations, individual-based simulations, and Markov chain methodology. In this paper, we: (1) identify component processes of avian reproduction; (2) review existing methods for modeling fecundity; (3) place these diverse models under a common conceptual framework; (4) describe the parameterization, validation, and limitations of such models; and (5) point out future considerations and challenges in the application of fecundity models. We hope this synthesis of existing literature will help direct researchers toward the most appropriate methods to assess avian reproductive success for answering questions in evolutionary ecology, natural history, population dynamics, reproductive toxicology, and management.     

Application of Markov-chain model for vegetation restoration assessment at landslide areas caused by a catastrophic earthquake in Central Taiwan

The 921 earthquake caused a catastrophic disaster in Central Taiwan. Ten years have passed since the earthquake occurred. Vegetation succession is the basis for establishing a restoration reference which plays an important role in vegetation restoration at landslide sites. Generally, growth conditions for grass are easier and the growth rate is faster than that for trees. Therefore, grass can be considered a pioneer species or an important reference for the early vegetation succession stage. This is the reason why grass is required to be extracted from other land covers. Integrating remote sensing, geographic information system and image classification into vegetation succession models is very important. In this study, the Markov chain model was applied for vegetation restoration assessment and discussion. Chiufenershan and Ninety-nine peaks were selected as the study areas. Five SPOT satellite images are used for land cover mapping and vegetation restoration simulations. Four categories of land covers were extracted, including forest, grass, bare land and water, respectively. From the transitive probability matrix (derived from any two land covers), the results show that vegetation restoration at the Chiufenershan and Ninety-nine peaks landslide areas is ongoing, but that has been disturbed by natural disasters.