低闭合油藏油水同层储层含水饱和度新模型

G地区P油层由于闭合高度低，油水分异差，存在大量的油水同层，且该区油水同层与油层的物性、电性相近，使得传统的利用电阻率和孔隙度计算含水饱和度的方法失效；加上工区开发过程中采取多层合试，单层试油且产液性质为油水同出的层位较少，可供选择进行油水同层饱和度建模的样本较少，使得该区油水同层饱和度的准确计算成为储量提交的难点。针对这一问题，提出以少量的密闭取芯井为基础样本，首先应用相渗资料建立起产水率与含水饱和度关系，然后外推到常规取芯井获得含水饱和度的补充样本，进而通过优选孔隙度、电阻率比值等建模参数，构建了适用于研究区油水同层的饱和度计算新模型，通过统计，其平均相对误差仅为3.59%，满足了储量计算的精度要求。     

Estimation of parameters in incomplete data models defined by dynamical systems

Parametric incomplete data models defined by ordinary differential equations (ODEs) are widely used in biostatistics to describe biological processes accurately. Their parameters are estimated on approximate models, whose regression functions are evaluated by a numerical integration method. Accurate and efficient estimations of these parameters are critical issues. This paper proposes parameter estimation methods involving either a stochastic approximation EM algorithm (SAEM) in the maximum likelihood estimation, or a Gibbs sampler in the Bayesian approach. Both algorithms involve the simulation of non-observed data with conditional distributions using Hastings–Metropolis (H–M) algorithms. A modified H–M algorithm, including an original local linearization scheme to solve the ODEs, is proposed to reduce the computational time significantly. The convergence on the approximate model of all these algorithms is proved. The errors induced by the numerical solving method on the conditional distribution, the likelihood and the posterior distribution are bounded. The Bayesian and maximum likelihood estimation methods are illustrated on a simulated pharmacokinetic nonlinear mixed-effects model defined by an ODE. Simulation results illustrate the ability of these algorithms to provide accurate estimates.     

Model-based clustering for social networks

Summary.  Network models are widely used to represent relations between interacting units or actors. Network data often exhibit transitivity, meaning that two actors that have ties to a third actor are more likely to be tied than actors that do not, homophily by attributes of the actors or dyads, and clustering. Interest often focuses on finding clusters of actors or ties, and the number of groups in the data is typically unknown. We propose a new model, the latent position cluster model , under which the probability of a tie between two actors depends on the distance between them in an unobserved Euclidean 'social space', and the actors' locations in the latent social space arise from a mixture of distributions, each corresponding to a cluster. We propose two estimation methods: a two-stage maximum likelihood method and a fully Bayesian method that uses Markov chain Monte Carlo sampling. The former is quicker and simpler, but the latter performs better. We also propose a Bayesian way of determining the number of clusters that are present by using approximate conditional Bayes factors. Our model represents transitivity, homophily by attributes and clustering simultaneously and does not require the number of clusters to be known. The model makes it easy to simulate realistic networks with clustering, which are potentially useful as inputs to models of more complex systems of which the network is part, such as epidemic models of infectious disease. We apply the model to two networks of social relations. A free software package in the R statistical language, latentnet, is available to analyse data by using the model.     

Two-Event Model for Carcinogenesis: Biological, Mathematical, and Statistical Considerations

A two-mutation model for carcinogenesis is reviewed. General principles in fitting the model to epidemiologic and experimental data are discussed, and some examples are given. A general solution to the model with time-dependent parameters is developed, and its use is illustrated by application to data from an experiment in which rats exposed to radon developed lung tumors.     

Hierarchical Generalized Linear Models and Frailty Models with Bayesian Nonparametric Mixing

This paper proposes Bayesian nonparametric mixing for some well-known and popular models. The distribution of the observations is assumed to contain an unknown mixed effects term which includes a fixed effects term, a function of the observed covariates, and an additive or multiplicative random effects term. Typically these random effects are assumed to be independent of the observed covariates and independent and identically distributed from a distribution from some known parametric family. This assumption may be suspect if either there is interaction between observed covariates and unobserved covariates or the fixed effects predictor of observed covariates is misspecified. Another cause for concern might be simply that the covariates affect more than just the location of the mixed effects distribution. As a consequence the distribution of the random effects could be highly irregular in modality and skewness leaving parametric families unable to model the distribution adequately. This paper therefore proposes a Bayesian nonparametric prior for the random effects to capture possible deviances in modality and skewness and to explore the observed covariates' effect on the distribution of the mixed effects.     

NONPARAMETRIC AUTOCOVARIANCE FUNCTION ESTIMATION

Nonparametric estimators of autocovariance functions for non-stationary time series are developed. The estimators are based on straightforward nonparametric mean function estimation ideas and allow use of any linear smoother (e.g. smoothing spline, local polynomial). The paper studies the properties of the estimators, and illustrates their usefulness through application to some meteorological and seismic time series.     

Measuring the complexity of generalized linear hierarchical models

Measuring a statistical model's complexity is important for model criticism and comparison. However, it is unclear how to do this for hierarchical models due to uncertainty about how to count the random effects. The authors develop a complexity measure for generalized linear hierarchical models based on linear model theory. They demonstrate the new measure for binomial and Poisson observables modeled using various hierarchical structures, including a longitudinal model and an areal‐data model having both spatial clustering and pure heterogeneity random effects. They compare their new measure to a Bayesian index of model complexity, the effective number p_D of parameters (Spiegelhalter, Best, Carlin & van der Linde 2002); the comparisons are made in the binomial and Poisson cases via simulation and two real data examples. The two measures are usually close, but differ markedly in some instances where p_D is arguably inappropriate. Finally, the authors show how the new measure can be used to approach the difficult task of specifying prior distributions for variance components, and in the process cast further doubt on the commonly‐used vague inverse gamma prior.     

AN ALGORITHMIC APPROACH TO BAYESIAN LINEAR MODEL CALCULATIONS

A framework is described for organizing and understanding the computations necessary to obtain the posterior mean of a vector of linear effects in a normal linear model, conditional on the parameters that determine covariance structure. The approach has two major uses; firstly, as a pedagogical tool in the derivation of formulae, and secondly, as a practical tool for developing computational strategies without needing complicated matrix formulae that are often unwieldy in complex hierarchical models. The proposed technique is based upon symbolic application of the sweep operator SWP to an appropriate tableau of means and covariances. The method is illustrated with standard linear model specifications, including the so-called mixed model, with both fixed and random effects.     

FL115离心式机油滤清器的特性研究与试验分析

建立了分流离心式滤清器转速特性和液力特性的数学模型.通过试验得到FL115离心式滤清器在不同喷嘴口径以及不同温度工况下的转速特性曲线和液力特性曲线,以及滤清效率.分析了转子转速、驱动流量和进油压力三者之间的关系,推出了设计喷嘴的最佳口径范围.通过理论数据与试验数据的比较,证明了该数学模型可以作为研发离心式滤清器的设计参考.     

试论足球专项速度耐力影响因素数学模型的建立

根据专项速度耐力水平高低与测试及其影响因素，提出用数学模型方法来简化这些问题，以达到更有效、更科学地控制运动员专项速度耐力的训练．数学模型的建立反映了运动员对专项速度耐力各影响因素综合能力