三江源地区天然草地牧草产量的Markov预测模型

Markov预测技术是应用Markov链的相关预测的基本原理与方法来研究分析时间序列的变化规律，并预测其未来变化趋势的一种预报方法，适用于随机波动较大的预报问题。根据Markov链原理，提出了一个用于三江源地区天然草地年平均牧草产量预报的离散随机过程模型。实测资料的验证结果表明，这种模型计算精度较高，具有良好的应用价值。     

运用Markov链对我国猪肉产量进行趋势预测

近几年猪肉供给的波动受到社会各方的普遍关注,对猪肉供给的预测显的尤为重要。学术界对猪肉供给的研究很多,但大都停留在定性的分析层面。本文采用定量方法对我国猪肉年度产量进行分析研究,将我国猪肉年度产量增速序列转化为不同的状态和状态的转移概率。用Markov链对2012年猪肉的产量进行预测,并用Markov链遍历性原理得到经过长期变化之后的年度增减率的数学期望,对猪肉供给的波动趋势进行了分析。     

南通城乡居民生活质量水平层次结构的预测分析

利用修正转移概率矩阵的Markov模型,预测分析南通城乡居民生活质量水平层次结构的变化趋势。结果表明,利用修正转移概率矩阵的Markov模型对南通城乡居民生活质量水平进行定量预测与分析,对历史数据样本数量要求不多,计算简便,且获取的计算结果更具客观性和真实性。     

金融市场随机波动：基于文献综述的视角

探讨了金融市场收益率存在历史、隐含和现实的三类随机波动现象,并呈现出尖峰厚尾、杠杆、集群、微笑、溢出、长记忆、信息流、共生波动等分布特征。进一步归纳了基于不同分布特征的随机波动的GARCH、SV、制度转换、阀值模型等模型,梳理出重点SV模型的三类估计方法：基于矩法、极大似然法估计和马尔科夫链蒙特卡罗（MCMC）方法,以及有效估计SV模型后,其在收益波动率预测、风险管理上的应用。     

“3S”技术在水土保持预测预报模型中的应用

基于“3S”技术的水土保持预测预报模型研究在国内外都是一项新的研究课题，本文通过结合国内外“3S”技术在水土保持预测预报中的应用现状，阐述了“3S”技术在水土保持模型中的意义和方法，并对“3S”技术在该领域的发展进行了展望．     

新疆草原蝗虫发生面积与大气环流特征量指数模型的研究

通过对1986-2003年新疆草原蝗虫发生面积与大气环流指数74项特征值的相关分析,筛选出与新疆蝗虫发生有显著关系的大气环流指数因子,采用逐步回归方法建立4个新疆蝗虫发生面积预测预报模型,并对模型进行了检验。利用模型对2004-2006年新疆蝗虫发生面积进行延伸预测,并与实际蝗虫发生面积进行比对,最终挑选出预报准确率在85％以上、对新疆草原蝗虫发生面积趋势具有一定预报能力和应用价值的模型,并初步分析了大气环流特征量与蝗虫发生面积的关系。     

两种线虫在牧草地上季节动态预测预报模拟模型的应用

两种线虫在牧草地上季节动态预测预报模拟模型的应用孟秀珍，沈杰，曹杰我们曾建立了捻转血矛线虫和粗纹食道口线虫在牧地上季节动态预测预报模拟模型［１，２］，由于宜昌县百里荒草畜示范场羊寄生虫优势虫种仍为这两种［３］，因此我们应用这两个模拟模型对百里荒牧地羊...     

基于混合pi-sigma网络的短期电力负荷预测

本文提出了一种短期电力负荷的混合pi-sigma模糊神经网络回归预测方法。该方法根据短期电力负荷的周期性,利用混合pisigma模糊神经推理功能,对欧洲电力负荷进行预测。该模型以高斯基函数作为模糊子集的隶属度函数,在线动态调整隶属度函数和结论参数。实例表明,本文提出的混合pi-sigma网络电力负荷预报方法优于常规时序预测方法,具有物理意义透明、预测操作方便,精确度高以及预测结果确定等特点,克服了神经网络电力负荷预报方法的不确定性。仿真实验结果验证了所提模型和方法的有效性。     

高寒草甸区土壤水分动态的模拟研究

土壤水分在植物生长期间的动态变化,可分解为周期项和随机波动项两个部分。利用1992年土壤水分观测资料,以谐波分析法对周期项进行随时间序列的模拟处理,以剩余土壤水分(随机波动项)建立与自然降水量的线性回归关系后,依加法模式确定高寒草甸地区土壤水分动态变化的预报模型方程为: 对1992年土壤水分资料进行回代模拟,拟合率很高,平均相对误差为7.2％。对1993年土壤水分动态变化进行预测预报,准确率较高,其相对误差平均为8.9％。结果表明,该模拟方程,能准确预报土壤水分动态变化的过程,进而对研究草地物质能量循环等生态过程均具有一定的实用价值。     

内蒙古草原火险等级短期预报研究

利用EOS/MODIS数据和内蒙古不同类型草地枯草期野外实测可燃物月动态数据,建立枯草期遥感估测模型。在此基础上,选择积雪覆盖、可燃物重量、草地连续度、日降水量、日最小相对湿度、日最高气温、日最大风速等7个指标,采用层次分析法确定各指标的权重,构建草原火险指数,建立草原火险等级短期预报模型。应用模型可将内蒙古草原的火险状态划分为不燃、难燃、可燃、易燃、极易燃5级,并对火险做出短期预报。利用数据抽样回代检验方法对草原火险等级短期预报进行精度检验,检验结果为落区预报准确率达96.42%,预报结果与实际基本相符,可以用于内蒙古草原火险短期预报的实际应用。     

Microcomputer programs for markov and modified markov chain disease models

Two simulation models were created using an electronic spreadsheet. The models, IV and V, were developed from a multi-agent mastisis example and assumed Markov and modified Markov chain processes, respectively. Model IV simulated disease occurrence in which the probability of transmission remained constant. Model V simulated disease occurrence in a population which had constant state transition probability rates, except for those of a single agent, which were assumed to be dynamic and follow the assumptions of the classic Reed-Frost model. The methodology developed for these models should be easily adopted to other disease problems in either human or veterinary medicine.     

Breeding objectives for beef cattle used in different production systems: 1. Model development

A bio-economic model was developed to evaluate utilization of beef bulls in a variety of production systems. The model can simulate life-cycle production of both beef and dairy cow herds with or without an integrated feedlot system. The Markov chain approach is used to simulate herd dynamics. The herd is described in terms of animal states and possible transitions among them. Equilibrium herd structures of the integrated production systems are calculated in their stationary states. The economic efficiency of each system is a function of biological traits of animals and of management and economic parameters. The model allows estimation of marginal economic values for 16 traits separately in each system. The economic weight for each trait or direct and maternal trait component in each selection group and breed of interest is then calculated as the weighted sum of the economic values for the trait in all production systems in which the selection group has an impact. Weighting factors for each system are computed as the product of the number of discounted expressions for direct and maternal trait components transmitted in that system by the selection group and the proportion of total cows belonging to each system.     

A Bayesian model for spatial wildlife disease prevalence data

The analysis of the geographical distribution of disease on the scale of geographic areas such as administrative boundaries plays an important role in veterinary epidemiology. Prevalence estimates of wildlife population surveys are often based on regional count data generated by sampling animals shot by hunters. The observed disease rate per spatial unit is not an useful estimate of the underlying disease prevalence due to different sample sizes and spatial dependencies between neighbouring areas. Therefore, it is necessary to account for extra-sample variation and spatial correlations in the data to produce more accurate maps of disease incidence. The detection of spatial patterns is complicated by missing data in many of the geographical areas as the complete coverage of all areas is nearly impossible in wildlife surveys. For this purpose a hierarchical Bayesian model in which structured and unstructured over dispersion is modelled explicitly in terms of spatial and non-spatial components was implemented by Markov chain Monte Carlo methods. The model was empirically compared with the results of a non-spatial beta-binomial model using surveillance data of pseudorabies virus infections of European wild boars (Sus scrofa scrofa L.) in the Federal State of Brandenburg, Germany.     

Optimal replacement and ranking of dairy cows determined by a hierarchic Markov process

A dairy cow replacement model based on the notion of a hierarchic Markov process is presented. A hierarchic Markov process is a series of Markov decision processes built together in one Markov decision process, called the main process.In the model a cow is described in terms of lactation number, stage of lactation, the level of milk yield during the previous and present lactation, the length of the calving interval, and the genetic class defined from the breeding value of the father. The criterion of optimality is the maximization of the present value under an infinite planning horizon. Revenues from milk, calves, and replaced cows, feed costs and costs of replacement heifers are considered.The future profitability calculated from the optimal solution is used for ranking of the cows in the herd. The genetic class makes it possible to include the heifers available for replacement in the ranking and to let the replacement decision depend on the genetic class of the heifers.It is concluded that the milk yield of previous lactation is not needed as a state variable when the other variables are present in the model.     

Seasonal variation of bulk milk somatic cell counts in UK dairy herds: investigations of the summer rise

Individual cow somatic cell count (SCC) patterns were explored over a one year period in 33 dairy herds to investigate the reason for a summer rise in bulk milk somatic cell counts (BMSCC). Cow test day somatic cell counts were categorised according to the magnitude of change since the previous test day reading, to examine which categories were responsible for the summer increase. Multilevel models using Markov chain Monte Carlo methods were specified to estimate the number of somatic cells/ml produced by different cell count categories. Stage of lactation and parity were accounted for in the models. There was an increase in the proportion of cows that remained above 200,000 cells/ml for two consecutive recordings in summer and this group of cows were responsible for 70.8% of the increase in somatic cells/ml produced from May to September compared with October to March. There was no evidence that a greater new infection rate (somatic cell counts moving from below 100,000 cells/ml to over 200,000 cells/ml) contributed to the increased summer bulk milk somatic cell counts. There was no indication that a general small increase in all somatic cell counts played an important role in the increased summer somatic cell counts. Markov chain Monte Carlo methods provided a valuable and flexible platform for parameter estimation in reasonably complex multilevel models.     

Bayesian reanalysis of a quantitative trait locus accounting for multiple environments by scaling in broilers

A Bayesian method was developed to handle QTL analyses of multiple experimental data of outbred populations with heterogeneity of variance between sexes for all random effects. The method employed a scaled reduced animal model with random polygenic and QTL allelic effects. A parsimonious model specification was applied by choosing assumptions regarding the covariance structure to limit the number of parameters to estimate. Markov chain Monte Carlo algorithms were applied to obtain marginal posterior densities. Simulation demonstrated that joint analysis of multiple environments is more powerful than separate single trait analyses of each environment. Measurements on broiler BW obtained from 2 experiments concerning growth efficiency and carcass traits were used to illustrate the method. The population consisted of 10 full-sib families from a cross between 2 broiler lines. Microsatellite genotypes were determined on generations 1 and 2, and phenotypes were collected on groups of generation 3 animals. The model included a polygenic correlation, which had a posterior mean of 0.70 in the analyses. The reanalysis agreed on the presence of a QTL in marker bracket MCW0058-LEI0071 accounting for 34% of the genetic variation in males and 24% in females in the growth efficiency experiment. In the carcass experiment, this QTL accounted for 19% of the genetic variation in males and 6% in females.     

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.     

Forecasting clinical disease in pigs: comparing a naive and a Bayesian approach

In veterinary practice the clinician often evaluates and predicts herd health status over time according to clinical criteria. In this paper, we modeled three different clinical signs among pigs based on longitudinal clinical observations in 15 pig herds. We compared and discussed the outputs from two different approaches for making clinical forecasts in a herd: a naive approach using a simple time series model with previous disease observations as predictors and a Bayesian state space models approach, in which the time lag variable entered into the random component of the model. We used the Markov chain Monte Carlo technique to calculate posterior distributions of the forecasts. For the herd specific forecasts the results showed that there were only minor differences between the forecasts from the simple time series model and the median forecasts from the Bayesian model. However, the credibility intervals from the Bayesian model were wider than the forecasts from the simple model and, therefore the Bayesian model encompassed the variability in the forecasts better. Compared to the statistical model, the simple time series would be easier to implement in a practical setting. However, the latter lacks the inherent “generality” from the statistical model that allows the user to make statements about the distribution of the herds and to predict disease status based on the “average” correlation among the herds. The applicability of the Bayesian approach within a clinical decision-making framework was discussed, with special emphasis on the use of prior information and clinical forecasting.     

Identifiability of parameters and behaviour of MCMC chains: a case study using the reaction norm model

Markov chain Monte Carlo (MCMC) enables fitting complex hierarchical models that may adequately reflect the process of data generation. Some of these models may contain more parameters than can be uniquely inferred from the distribution of the data, causing non‐identifiability. The reaction norm model with unknown covariates (RNUC) is a model in which unknown environmental effects can be inferred jointly with the remaining parameters. The problem of identifiability of parameters at the level of the likelihood and the associated behaviour of MCMC chains were discussed using the RNUC as an example. It was shown theoretically that when environmental effects (covariates) are considered as random effects, estimable functions of the fixed effects, (co)variance components and genetic effects are identifiable as well as the environmental effects. When the environmental effects are treated as fixed and there are other fixed factors in the model, the contrasts involving environmental effects, the variance of environmental sensitivities (genetic slopes) and the residual variance are the only identifiable parameters. These different identifiability scenarios were generated by changing the formulation of the model and the structure of the data and the models were then implemented via MCMC. The output of MCMC sampling schemes was interpreted in the light of the theoretical findings. The erratic behaviour of the MCMC chains was shown to be associated with identifiability problems in the likelihood, despite propriety of posterior distributions, achieved by arbitrarily chosen uniform (bounded) priors. In some cases, very long chains were needed before the pattern of behaviour of the chain may signal the existence of problems. The paper serves as a warning concerning the implementation of complex models where identifiability problems can be difficult to detect a priori. We conclude that it would be good practice to experiment with a proposed model and to understand its features before embarking on a full MCMC implementation.