Accelerating inference for diffusions observed with measurement error and large sample sizes using approximate Bayesian computation

In recent years, dynamical modelling has been provided with a range of breakthrough methods to perform exact Bayesian inference. However, it is often computationally unfeasible to apply exact statistical methodologies in the context of large data sets and complex models. This paper considers a nonlinear stochastic differential equation model observed with correlated measurement errors and an application to protein folding modelling. An approximate Bayesian computation (ABC)-MCMC algorithm is suggested to allow inference for model parameters within reasonable time constraints. The ABC algorithm uses simulations of ‘subsamples’ from the assumed data-generating model as well as a so-called ‘early-rejection’ strategy to speed up computations in the ABC-MCMC sampler. Using a considerate amount of subsamples does not seem to degrade the quality of the inferential results for the considered applications. A simulation study is conducted to compare our strategy with exact Bayesian inference, the latter resulting two orders of magnitude slower than ABC-MCMC for the considered set-up. Finally, the ABC algorithm is applied to a large size protein data. The suggested methodology is fairly general and not limited to the exemplified model and data.     

Semi-empirical likelihood inference for the ROC curve with missing data

The receiver operating characteristic (ROC) curve is one of the most commonly used methods to compare the diagnostic performance of two or more laboratory or diagnostic tests. In this paper, we propose semi-empirical likelihood based confidence intervals for ROC curves of two populations, where one population is parametric and the other one is non-parametric and both have missing data. After imputing missing values, we derive the semi-empirical likelihood ratio statistic and the corresponding likelihood equations. It is shown that the log-semi-empirical likelihood ratio statistic is asymptotically scaled chi-squared. The estimating equations are solved simultaneously to obtain the estimated lower and upper bounds of semi-empirical likelihood confidence intervals. We conduct extensive simulation studies to evaluate the finite sample performance of the proposed empirical likelihood confidence intervals with various sample sizes and different missing probabilities.     

陕西省人口城市化Logistic模型及其应用——基于结构突变的理论分析

城市化是走向现代化的必经阶段,准确的城市化预测是进行经济、社会建设的基础。在结构突变理论的基础上,用Logistic模型对1978～2010年陕西城市化率进行分析。结论表明：1999年为陕西城市化率的结构突变点,说明城市化率的增长受到外部冲击的影响,分段以后的拟合优度明显提高。分别以阈值0.8和1进行分阶段构建的Logistic拟合精度明显提高,但阈值为1的精度更高,说明陕西城市化还在加速,预测表明到2030年陕西城市化率将达到70%左右。总体而言,从1984年到2030年为陕西省城市化的加速阶段。城市化加速阶段的住房问题、人口膨胀、环境恶化、交通拥挤、社会治安问题必须妥善解决。     

Dividend barrier and ruin problems for a risk model with delayed claims

In this paper, a compound Poisson risk model in the presence of a constant dividend barrier is considered. Two types of individual claims, main claims and by-claims, are defined, where every by-claim is induced by the main claim and and the time of delay for the claim is assumed to be random. A system of integro-differential equations with certain boundary conditions for the expected discounted penalty function is derived. We show that its solution can be expressed as the solution to the expected discounted penalty function in the same risk model with the absence of a barrier plus a linear combination of two linearly independent solutions to the associated homogeneous integro-differential equation. Using systems of integro-differential equations for the moment-generating function as well as for the arbitrary moments of the sum of discounted dividend payments until ruin, a matrix version of the dividends–penalty type relationship is derived. We also prove that ruin is certain under constant dividend barrier strategy. The closed form expressions are given when the claim amounts from both classes are exponentially distributed. Finally, a numerical example is presented to illustrate the solution procedure.     

邓小平社会主义核心价值观教育思想探析

以泰州某大跨度连续梁桥的静动载试验为例，建立ANSYS和桥梁博士模型进行静动力有限元数值计算。将试验结果与模型计算值进行比较，试验结果表明,该桥结构刚度和承载能力满足设计要求。     

Bayesian penalized B-spline estimation approach for epidemic models

Ordinary differential equations (ODEs) are normally used to model dynamic processes in applied sciences such as biology, engineering, physics, and many other areas. In these models, the parameters are usually unknown, and thus they are often specified artificially or empirically. Alternatively, a feasible method is to estimate the parameters based on observed data. In this study, we propose a Bayesian penalized B-spline approach to estimate the parameters and initial values for ODEs used in epidemiology. We evaluated the efficiency of the proposed method based on simulations using the Markov chain Monte Carlo algorithm for the Kermack–McKendrick model. The proposed approach is also illustrated based on a real application to the transmission dynamics of hepatitis C virus in mainland China.     

服装系列设计方法之“抽象方程”论

通过长期的实践教学经验总结,将服装系列设计方法与数学方程联系在一起,形成服装系列设计的"抽象方程"理论,使服装系列设计具有了定向、定量、明确、有序的特征,力求寻找一条由简到繁、由易到难、循序渐进的学习实践方法,帮助服装设计初学者尽早摆脱设计瓶颈,步入设计正轨。     

Estimation of parameters of SDE driven by fractional Brownian motion with polynomial drift

ABSTRACT

Strongly consistent and asymptotically normal estimators of the Hurst index and volatility parameters of solutions of stochastic differential equations with polynomial drift are proposed. The estimators are based on discrete observations of the underlying processes.     

雾霾感知风险与公众应对行为的实证分析

通过在雾霾严重时期收集的大规模问卷调查数据,建立了雾霾感知风险等因素与应对行为之间关系的结构方程模型.分析显示,对环境信息越敏感、雾霾感知风险越大、对雾霾知识了解越多、雾霾感知可控性越大的公众会采取更多的防护与应对措施,他们对相关防护产品的购买意愿也越强.特别是,感知风险在环境信息与应对行为以及环境满意度之间起着重要的中介变量作用,即当雾霾污染引起人们的感知风险时,会促使他们采取更多的应对行为,并且对环境满意度评价产生负面影响.另外,雾霾感知可控性在雾霾知识熟悉度与应对行为以及环境满意度之间起着部分中介变量的作用.     

State‐led industrial development,structural transformation and elite‐led plunder: Angola (2002–2013) as a developmental state

From 2002 to 2013, Angola engaged in large‐scale state‐led reconstruction and development alongside an elite‐led appropriation and seizure of national assets. Until the oil price shock, Angola had been succeeding in promoting rapid economic growth, and possibly even significant social development, alongside a massive grab of wealth and power by local elites. Today, though an economic crisis has taken hold, frequent predictions of the country's imminent collapse have yet to be fulfilled. This article reviews the state's development planning and expenditure with a focus on public investment and industrial development to determine to what extent Angola during this period might be considered a developmental or petro‐developmental state. It is argued that, while more significant than generally thought, petro‐developmental outcomes were and are limited by the autocratic and neopatrimonial tendencies of the Angolan elite. Nevertheless, limited success with structural transformation may have lasting effects. Following its long civil war, the conditions existed for Angola to follow a new path of state‐led development. Though it may now be more difficult, structural transformation and economic diversification remain the only path to economic and social development.