多重填补法Markov Chain Monte Carlo模型在有缺失值的妇幼卫生纵向数据中的应用

目的 针对妇幼卫生纵向数据的任意缺失模式,采用多重填补方法进行填补,探求最佳填补结果,以便对数据作进一步分析与研究。方法 运用SAS9.0 ,采用多重填补方法Markov China Monte Carlo(MCMC)模型对缺失数据进行多次填补并综合分析。结果 填补5次所得结果最优。结论 多重填补方法可以处理有缺失数据资料中的许多普遍问题,可提高统计效率,尤其是MCMC模型在处理复杂的缺失数据上,优势明显。

基于Markov Chain Monte Carlo模型对医院调查资料中缺失数据的多重估算

目的探讨基于Markov Chain Monte Carlo(MCMC)模型的多重估算法在处理医院调查资料缺失数据中的应用。方法运用SAS9.2编写程序,在分析数据的分布类型和缺失机制的基础上,采用MCMC法对缺失数据进行多次填补和联合统计推断,分析多重估算法的优势。结果数据服从多元正态分布与随机缺失,采用MCMC法填补10次所得的结果最佳。结论多重估算既可反映缺失数据的不确定性,又可充分利用现有资料的信息、提高统计效率、对模型的估计结果更加可信,是处理缺失数据的有效方法。

基于Monte Carlo法的苯乙烯-丙烯腈单链模拟

聚合物链组成和分布对聚合物的性能具有十分重要的意义。基于此,本文参考某企业的单体配方,首先建立了二元共聚链增长模型,并采用Monte Carlo法对苯乙烯-丙烯腈共聚单链的链增长过程进行了模拟,分析对比了单体比对转化率及丙烯腈结合率的影响,考察了分批加料对链结构均匀性的影响。结果表明:当转化率高于91%时,丙烯腈结合率的变化率大于0.5%,造成共聚物分布不均;在考察的单体比范围内,原料中丙烯腈含量越低(大于25%),展现出来的共聚产物越均匀,可调节的转化率范围就越宽;当原料中丙烯腈为27%~35%,转化率在85.0%以上时,丙烯腈瞬时结合率的变化率仅在±0.5%的范围内波动,且丙烯腈平均结合率的变化小于1%;分批进料能有效提高共聚物的链结构均匀性,当单体比为67/33的转化率由91%提升至98%时,丙烯腈瞬时结合率的变化率小于±0.5%,且丙烯腈平均结合率的变化小于1%。上述研究结果为其他类似体系研究及工业生产稳定产品提供了一定的数据基础和理论指导。

Bayesian Markov chain Monte Carlo inversion for anisotropy of PP-and PS-wave in weakly anisotropic and heterogeneous media

A single set of vertically aligned cracks embedded in a purely isotropic background may be con- sidered as a long-wavelength effective transversely iso- tropy （HTI） medium with a horizontal symmetry axis. The crack-induced HTI anisotropy can be characterized by the weakly anisotropic parameters introduced by Thomsen. The seismic scattering theory can be utilized for the inversion for the anisotropic parameters in weakly aniso- tropic and heterogeneous HTI media. Based on the seismic scattering theory, we first derived the linearized PP- and PS-wave reflection coefficients in terms of P- and S-wave impedances, density as well as three anisotropic parameters in HTI media. Then, we proposed a novel Bayesian Mar- kov chain Monte Carlo inversion method of PP- and PS- wave for six elastic and anisotropic parameters directly. Tests on synthetic azimuthal seismic data contaminated by random errors demonstrated that this method appears more accurate, anti-noise and stable owing to the usage of the constrained PS-wave compared with the standards inver- sion scheme taking only the PP-wave into account.

Monte Carlo Simulations of Density Profiles for Hard-Sphere Chain Fluids Confined Between Surfaces

Covering a wide range of bulk densities, density profiles for hard-sphere chain fluids (HSCFs) with chain length of 3,4,8,20,32 and 64 confined between two surfaces were obtained by Monte Carlo simulations using extended continuum configurational-bias (ECCB) method. It is shown that the enrichment of beads near surfaces is happened at high densities due to the bulk packing effect, on the contrary, the depletion is revealed at low densities owing to the configurational entropic contribution. Comparisons with those calculated by density functional theory presented by Cai et al. indicate that the agreement between simulations and predictions is good. Compressibility factors of bulk HSCFs calculated using volume fractions at surfaces were also used to test the reliability of various equations of state of HSCFs by different authors.

Seismic fluid identification using a nonlinear elastic impedance inversion method based on a fast Markov chain Monte Carlo method

Elastic impedance inversion with high efficiency and high stability has become one of the main directions of seismic pre-stack inversion. The nonlinear elastic impedance inversion method based on a fast Markov chain Monte Carlo （MCMC） method is proposed in this paper, combining conventional MCMC method based on global optimization with a preconditioned conjugate gradient （PCG） algorithm based on local optimization, so this method does not depend strongly on the initial model. It converges to the global optimum quickly and efficiently on the condition that effi- ciency and stability of inversion are both taken into consid- eration at the same time. The test data verify the feasibility and robustness of the method, and based on this method, we extract the effective pore-fluid bulk modulus, which is applied to reservoir fluid identification and detection, and consequently, a better result has been achieved.

Evaluation of the Reliability of a System: Approach by Monte Carlo Simulation and Application

The objective of this paper is to evaluate the reliability of a system in its different states (absence of failures, partial failure and total failure) and to propose actions to improve this reliability by an approach based on Monte Carlo simulation. It consists of a probabilistic evaluation based on Markov Chains. In order to achieve this goal, the functionalities of Markov Chains and Monte Carlo simulation steps are deployed. The application is made on a production system. .

SEMI-BLIND CHANNEL ESTIMATION OF MULTIPLE-INPUT/MULTIPLE-OUTPUT SYSTEMS BASED ON MARKOV CHAIN MONTE CARLO METHODS

This paper addresses the issues of channel estimation in a Multiple-Input/Multiple-Output (MIMO) system. Markov Chain Monte Carlo (MCMC) method is employed to jointly estimate the Channel State Information (CSI) and the transmitted signals. The deduced algorithms can work well under circumstances of low Signal-to-Noise Ratio (SNR). Simulation results are presented to demonstrate their effectiveness.

MONTE CARLO STUDY ON THE CRITICAL ADSORPTION POINT OF BONDFLUCTUATED POLYMER CHAINS TETHERED ON ADSORBING SURFACES

The behavior of three-dimensional bond fluctuation model chains tethered on an adsorbing fiat surface was simulated by the Monte Carlo method.The dependence of the number of surface contacts M on the interaction strengthεand the chain length N was investigated by a finite-size scaling law M = N;[a;+a;N;κ+ O((N;κ);)]forεnear the critical adsorption pointε;,i.e.,κ=（ε-ε;）/ε;closes to 0.The critical adsorption point was estimated to beε;=0.93,and the exponentsφ= 0.49 and l/v= 0.57.

DYNAMIC MONTE CARLO STUDY ON THE CORRELATION BETWEEN SHAPE AND SIZE OF LINEAR POLYMER CHAINS

The correlation between shape and size of linear chains on the simple cubic lattice is investigated using a dynamicMonte Carlo technique. A positive correlation between the asphericity parameter A and the square of the end-to-end distanceR^2, as well as that between A and the square of the radius of gyration S^2, is found for both RW and SAW chains, indicatingthat a chain conformation of small size is usually more spherical than one of large size. The result can explain why the shapeof the SAW chain deviate much more from a sphere than that of the RW chain, and can also explain the similar dependenceof size and shape on chain stiffness and on the distance of the first bead of a chain from an infinitely large flat surface.

Effective-field and Monte Carlo studies of mixed spin-2 and spin-1/2 Ising diamond chain

The magnetic properties of a mixed spin-2 and spin-1/2 ferromagnetic diamond chain are studied by effective-field theory and Monte Carlo（MC） simulation based on the Ising model.The temperature dependences of magnetization,magnetic susceptibility,internal energy,and specific heat are studied,respectively.The exchange interaction dependences of magnetization and the critical temperature are calculated by MC simulation.The changes of magnetization depending on the field increasing and then the field decreasing under steady-static conditions are also given.

On Finding the Smallest Generalized Eigenpair Using Markov Chain Monte Carlo Algorithm

This paper proposes a new technique based on inverse Markov chain Monte Carlo algorithm for finding the smallest generalized eigenpair of the large scale matrices. Some numerical examples show that the proposed method is efficient.

Quantum Monte Carlo Study of Frustrated Spin Chain under External Field

In this paper a stochastic series expansion quantum Monte Carlo algorithm is used to study a frustratedspin chain with diagonal next-nearest-neighbor interactions.The detailed balance conditions are carefully analyzed toimprove the efficiency of simulation process.As an application of this algothrim,the total magnetization,the staticstructure factor and spin-stiffness are calculated for a certain set of system parameters as a function of external fieldstrength.

Monte Carlo Study on Spontaneous Recoil of Confined DNA Chain

A part of a long DNA chain was driven into a confined environment by an electric field, while the rest remains in the higher-entropy region. Upon removal of the field, the chain recoils to the higher-entropy region spontaneously. This dynamical process was investigated by Monte Carlo simulations. The simulation reproduces the experimentally-observed phenomenon that the recoil of the DNA chain is initially slow and gradually increases in speed due to the presence of the confinement-entropic force. The results show that with increasing the dimension or decreasing the spacing of the nanopillars the recoil velocity of the DNA chain will increase. Further analysis suggests that the characteristic entropy per monomer in the confinement is proportional to the area fraction of the free part in the confinement.

Dynamic Monte Carlo study on the probability distribution functions of tail-like polymer chain

The configurational properties of tail-like polymer chains with one end attached to a flat surface are studied by using dynamic Monte Carlo technique. We find that the probability distribution of the free end in z direction P（Rz） and the density profile p（z） can be scaled approximately by a factor β to be a length independent function for both random walking （RW） and self-avoiding walking （SAW） tail-like chains, where the factor β is related to the mean square end-to-end distance 〈RE〉. The scaled P（Rz） of the SAW chain roughly overlaps that of the RW chain, but the scaled p（z） of the SAW chain locates at smaller βz than that of the RW chain.

Potential-Decomposition Strategy in Markov Chain Monte Carlo Sampling Algorithms

We introduce the potential-decomposition strategy （PDS）, which can be used in Markov chain Monte Carlo sampling algorithms. PDS can be designed to make particles move in a modified potential that favors diffusion in phase space, then, by rejecting some trial samples, the target distributions can be sampled in an unbiased manner. Furthermore, if the accepted trial samples are insumcient, they can be recycled as initial states to form more unbiased samples. This strategy can greatly improve efficiency when the original potential has multiple metastable states separated by large barriers. We apply PDS to the 2d Ising model and a double-well potential model with a large barrier, demonstrating in these two representative examples that convergence is accelerated by orders of magnitude.

Markov Chain Monte Carlo Solution of Laplace’s Equation in Axisymmetric Homogeneous Domain

With increasing complexity of today’s electromagnetic problems, the need and opportunity to reduce domain sizes, memory requirement, computational time and possibility of errors abound for symmetric domains. With several competing computational methods in recent times, methods with little or no iterations are generally preferred as they tend to consume less computer memory resources and time. This paper presents the application of simple and efficient Markov Chain Monte Carlo (MCMC) method to the Laplace’s equation in axisymmetric homogeneous domains. Two cases of axisymmetric homogeneous problems are considered. Simulation results for analytical, finite difference and MCMC solutions are reported. The results obtained from the MCMC method agree with analytical and finite difference solutions. However, the MCMC method has the advantage that its implementation is simple and fast.

AN IMPROVED MARKOV CHAIN MONTE CARLO METHOD FOR MIMO ITERATIVE DETECTION AND DECODING

Recently, a new soft-in soft-out detection algorithm based on the Markov Chain Monte Carlo (MCMC) simulation technique for Multiple-Input Multiple-Output (MIMO) systems is proposed, which is shown to perform significantly better than their sphere decoding counterparts with relatively low complexity. However, the MCMC simulator is likely to get trapped in a fixed state when the channel SNR is high, thus lots of repetitive samples are observed and the accuracy of A Posteriori Probability (APP) estimation deteriorates. To solve this problem, an improved version of MCMC simulator, named forced-dispersed MCMC algorithm is proposed. Based on the a posteriori variance of each bit, the Gibbs sampler is monitored. Once the trapped state is detected, the sample is dispersed intentionally according to the a posteriori variance. Extensive simulation shows that, compared with the existing solution, the proposed algorithm enables the markov chain to travel more states, which ensures a near-optimal performance.

Arriving at estimates of a rate and state fault friction model parameter using Bayesian inference and Markov chain Monte Carlo

The critical slip distance in rate and state model for fault friction in the study of potential earthquakes can vary wildly from micrometers to few me-ters depending on the length scale of the critically stressed fault.This makes it incredibly important to construct an inversion framework that provides good estimates of the critical slip distance purely based on the observed ac-celeration at the seismogram.To eventually construct a framework that takes noisy seismogram acceleration data as input and spits out robust estimates of critical slip distance as the output,we first present the performance of the framework for synthetic data.The framework is based on Bayesian inference and Markov chain Monte Carlo methods.The synthetic data is generated by adding noise to the acceleration output of spring-slider-damper idealization of the rate and state model as the forward model.

利用Monte Carlo技术模拟研究不同缺失值处理方法对完全随机缺失数据的处理效果

目的 以医疗卫生机构年报资料为数据来源,采用成组删除法、极大似然估计法、多重填补法分别对模拟的完全随机缺失数据集缺失值进行处理,比较不同缺失率下三种方法的缺失处理效果。方法 运用SAS9.3,采用Monte Carlo技术模拟完整数据集及不同缺失比例数据集,利用成组删除法、EM算法、MCMC算法对缺失数据进行处理,得到不同处理方法后的参数估计结果,与完整数据集参数估计进行比较。结果 对于完全随机缺失数据,不同缺失率下,成组删除法的准确率均比较好;缺失率小于10%,三种方法处理效果差异不大;缺失率在10%-30%,成组删除法精确度逐渐降低,EM与MCMC准确度与精确度较好,缺失率大于30%,MCMC准确度与精确度相对较好。结论 对于不同缺失率的数据,综合考虑准确度和精确度,采用不同的方法进行处理。