Random walk in an inhomogeneous medium with local impurities

In spite of Sinai's result that the decay of the velocity autocorrelation function for a random walk on ^d (d=2) can drastically change if local impurities are present, it is shown that local impurities can not abolish weak convergence to the Brownian motion if d2.     

随机模糊集与随机集

本文研究了三个方面的工作：一是定义了一种模糊集上的可测结构，从而定义了随机模糊集，这些定义都与论域Ｘ上的拓扑结构无关。将通常意义下的集合看成特殊模糊集得到的通常集合上的超可测结构与文（３）中的定义一致；二是给出了随机模糊集、随机集的一些等价条件；三是研究了随机模糊集、随机集的分布与其有限维落影族的关系。     

基于毛竹叶片理化参数的刚竹毒蛾危害检测研究

虫害检测算法研究是开展虫害快速、准确监测，制定精准森防检疫措施的重要基础。以毛竹叶片为研究尺度，基于刚竹毒蛾危害下的寄主外部形态与内部生理现象总结，选择并实测叶损量LL、相对叶绿素含量RCC、相对含水量RWC、原始光谱的733.66~898.56 nm值(ρ_{733.66~898.56})、一阶微分光谱的562.95~585.25 nm值(ρ′_{562.95~585.25})与706.18~725.41 nm值(ρ′_{706.18~725.41})等理化参数，随机划分实验组(63组)和验证组(37组)并设计5次重复实验；分别运用Fisher判别分析、BP神经网络、随机森林等三种方法建立刚竹毒蛾危害等级的检测模型，从检测精度、Kappa系数及R2等指标对模型的检测效果予以分析和比较。结果显示，Fisher判别分析、BP神经网络、随机森林的检测精度分别为69.19%，65.41%，83.78%，Kappa系数分别为0.576 9，0.532 4和0.778 8，R2分别为0.722 2，0.582 6和0.870 9，总体而言，三种方法均具备刚竹毒蛾危害的检测能力，随机森林的检测效果最优，Fisher判别分析次之，再次为BP神经网络；从分等级来看，随机森林的检测精度亦优于Fisher判别分析与BP神经网络，但3种方法对中度危害等级的检测精度均有所不足。该成果可为刚竹毒蛾危害及其他病虫害检测算法的选择提供参考，并为进一步建立冠层、遥感影像像元等尺度的虫害检测模型奠定基础。     

Random frog: An efficient reversible jump Markov Chain Monte Carlo-like approach for variable selection with applications to gene selection and disease classification

The identification of disease-relevant genes represents a challenge in microarray-based disease diagnosis where the sample size is often limited. Among established methods, reversible jump Markov Chain Monte Carlo (RJMCMC) methods have proven to be quite promising for variable selection. However, the design and application of an RJMCMC algorithm requires, for example, special criteria for prior distributions. Also, the simulation from joint posterior distributions of models is computationally extensive, and may even be mathematically intractable. These disadvantages may limit the applications of RJMCMC algorithms. Therefore, the development of algorithms that possess the advantages of RJMCMC methods and are also efficient and easy to follow for selecting disease-associated genes is required. Here we report a RJMCMC-like method, called random frog that possesses the advantages of RJMCMC methods and is much easier to implement. Using the colon and the estrogen gene expression datasets, we show that random frog is effective in identifying discriminating genes. The top 2 ranked genes for colon and estrogen are Z50753, U00968, and Y10871_at, Z22536_at, respectively. (The source codes with GNU General Public License Version 2.0 are freely available to non-commercial users at: http://code.google.com/p/randomfrog/.)     

A perturbed martingale approach to global optimization

A new global stochastic search, guided mainly through derivative-free directional information computable from the sample statistical moments of the design variables within a Monte Carlo setup, is proposed. The search is aided by imparting to the directional update term additional layers of random perturbations referred to as ‘coalescence’ and ‘scrambling’. A selection step, constituting yet another avenue for random perturbation, completes the global search. The direction-driven nature of the search is manifest in the local extremization and coalescence components, which are posed as martingale problems that yield gain-like update terms upon discretization. As anticipated and numerically demonstrated, to a limited extent, against the problem of parameter recovery given the chaotic response histories of a couple of nonlinear oscillators, the proposed method appears to offer a more rational, more accurate and faster alternative to most available evolutionary schemes, prominently the particle swarm optimization.     

Rejoinder on “Statistical reasoning with set-valued information: Ontic vs. epistemic views”

This note replies to comments made on our contribution to the Low Quality Data debate.     

Combinatorial and approximative analyses in a spatially random division process

For a spatial characteristic, there exist commonly fat-tail frequency distributions of fragment-size and -mass of glass, areas enclosed by city roads, and pore size/volume in random packings. In order to give a new analytical approach for the distributions, we consider a simple model which constructs a fractal-like hierarchical network based on random divisions of rectangles. The stochastic process makes a Markov chain and corresponds to directional random walks with splitting into four particles. We derive a combinatorial analytical form and its continuous approximation for the distribution of rectangle areas, and numerically show a good fitting with the actual distribution in the averaging behavior of the divisions.     

Operational issues and network effects in vaccine markets

One of the most important concerns for managing public health is the prevention of infectious diseases. Although vaccines provide the most effective means for preventing infectious diseases, there are two main reasons why it is often difficult to reach a socially optimal level of vaccine coverage: (i) the emergence of operational issues (such as yield uncertainty) on the supply side, and (ii) the existence of negative network effects on the consumption side. In particular, uncertainties about production yield and vaccine imperfections often make manufacturing some vaccines a risky process and may lead the manufacturer to produce below the socially optimal level. At the same time, negative network effects provide incentives to potential consumers to free ride off the immunity of the vaccinated population. In this research, we consider how a central policy-maker can induce a socially optimal vaccine coverage through the use of incentives to both consumers and the vaccine manufacturer. We consider a monopoly market for an imperfect vaccine; we show that a fixed two-part subsidy is unable to coordinate the market, but derive a two-part menu of subsidies that leads to a socially efficient level of coverage.     

Collective risk models with dependence

In actuarial science, collective risk models, in which the aggregate claim amount of a portfolio is defined in terms of random sums, play a crucial role. In these models, it is common to assume that the number of claims and their amounts are independent, even if this might not always be the case. We consider collective risk models with different dependence structures. Due to the importance of such risk models in an actuarial setting, we first investigate a collective risk model with dependence involving the family of multivariate mixed Erlang distributions. Other models based on mixtures involving bivariate and multivariate copulas in a more general setting are then presented. These different structures allow to link the number of claims to each claim amount, and to quantify the aggregate claim loss. Then, we use Archimedean and hierarchical Archimedean copulas in collective risk models, to model the dependence between the claim number random variable and the claim amount random variables involved in the random sum. Such dependence structures allow us to derive a computational methodology for the assessment of the aggregate claim amount. While being very flexible, this methodology is easy to implement, and can easily fit more complicated hierarchical structures.     

Orbits in a stochastic Goodwin–Lotka–Volterra model

This paper examines the cycling behavior of a deterministic and a stochastic version of the economic interpretation of the Lotka–Volterra model, the Goodwin model. We provide a characterization of orbits in the deterministic highly non-linear model. We then study a stochastic version, with Brownian noise introduced via a heterogeneous productivity factor. Existence conditions for a solution to the system are provided. We prove that the system produces cycles around a unique equilibrium point in finite time for general volatility levels, using stochastic Lyapunov techniques for recurrent domains. Numerical insights are provided.