On the Convergence of the Monte Carlo Maximum Likelihood Method for Latent Variable Models

While much used in practice, latent variable models raise challenging estimation problems due to the intractability of their likelihood. Monte Carlo maximum likelihood (MCML), as proposed by Geyer & Thompson (1992 ), is a simulation-based approach to maximum likelihood approximation applicable to general latent variable models. MCML can be described as an importance sampling method in which the likelihood ratio is approximated by Monte Carlo averages of importance ratios simulated from the complete data model corresponding to an arbitrary value of the unknown parameter. This paper studies the asymptotic (in the number of observations) performance of the MCML method in the case of latent variable models with independent observations. This is in contrast with previous works on the same topic which only considered conditional convergence to the maximum likelihood estimator, for a fixed set of observations. A first important result is that when is fixed, the MCML method can only be consistent if the number of simulations grows exponentially fast with the number of observations. If on the other hand, is obtained from a consistent sequence of estimates of the unknown parameter, then the requirements on the number of simulations are shown to be much weaker.     

Estimation of generalized linear latent variable models

Summary.  Generalized linear latent variable models (GLLVMs), as defined by Bartholomew and Knott, enable modelling of relationships between manifest and latent variables. They extend structural equation modelling techniques, which are powerful tools in the social sciences. However, because of the complexity of the log-likelihood function of a GLLVM, an approximation such as numerical integration must be used for inference. This can limit drastically the number of variables in the model and can lead to biased estimators. We propose a new estimator for the parameters of a GLLVM, based on a Laplace approximation to the likelihood function and which can be computed even for models with a large number of variables. The new estimator can be viewed as an M -estimator, leading to readily available asymptotic properties and correct inference. A simulation study shows its excellent finite sample properties, in particular when compared with a well-established approach such as LISREL. A real data example on the measurement of wealth for the computation of multidimensional inequality is analysed to highlight the importance of the methodology.     

Estimating household structure in ancient China by using historical data: a latent class analysis of partially missing patterns

Summary.  Social data often contain missing information. The problem is inevitably severe when analysing historical data. Conventionally, researchers analyse complete records only. Listwise deletion not only reduces the effective sample size but also may result in biased estimation, depending on the missingness mechanism. We analyse household types by using population registers from ancient China (618–907 AD) by comparing a simple classification, a latent class model of the complete data and a latent class model of the complete and partially missing data assuming four types of ignorable and non-ignorable missingness mechanisms. The findings show that either a frequency classification or a latent class analysis using the complete records only yielded biased estimates and incorrect conclusions in the presence of partially missing data of a non-ignorable mechanism. Although simply assuming ignorable or non-ignorable missing data produced consistently similarly higher estimates of the proportion of complex households, a specification of the relationship between the latent variable and the degree of missingness by a row effect uniform association model helped to capture the missingness mechanism better and improved the model fit.     

冗余度机器人的运动规划碰撞算法

在考虑了操作机的关节极限、自碰撞和静态障碍物的情况下,从给定的初始位形出发,发现一条到末端效应器目标位置和姿态的相连可到达路径。方法给出了机器人操作机点到点逆运动学问题求解算法,利用碰撞算法实现了冗余度机器人运动规划,仿真验证了该方法的有效性,并表明了该方法具有较大的实用价值。     

Bayesian analysis of a marked point process: Application in seismic hazard assessment

Point processes are the stochastic models most suitable for describing physical phenomena that appear at irregularly spaced times, such as the earthquakes. These processes are uniquely characterized by their conditional intensity, that is, by the probability that an event will occur in the infinitesimal interval (t, t+Δt), given the history of the process up tot. The seismic phenomenon displays different behaviours on different time and size scales; in particular, the occurrence of destructive shocks over some centuries in a seismogenic region may be explained by the elastic rebound theory. This theory has inspired the so-called stress release models: their conditional intensity translates the idea that an earthquake produces a sudden decrease in the amount of strain accumulated gradually over time along a fault, and the subsequent event occurs when the stress exceeds the strength of the medium. This study has a double objective: the formulation of these models in the Bayesian framework, and the assignment to each event of a mark, that is its magnitude, modelled through a distribution that depends at timet on the stress level accumulated up to that instant. The resulting parameter space is constrained and dependent on the data, complicating Bayesian computation and analysis. We have resorted to Monte Carlo methods to solve these problems.     

具扩充Jacobi结点的Lagrange插值逼近

研究了以扩充Jacobi多项式(1+x)Vn(x)的零点为基点的Lagrange插值多项式Ln(f,x)逼近/k)的一些问题.     

非负权最短路问题的一种简便算法

提出了非负权最短路问题的一种新算法。与有名的Ｄｉｊｋｓｔｒａ算法相比，这种算法计算简便、容易理解、易于编程。     

基于遗传算法的有柔性路径的动态调度问题研究

建立了有柔性路径的FMS动态调度问题的模型．采用离线重调度的方法，提出一种结合离线重调度两种生成调度方式的方法来阐述FMS的有柔性路径动态调度问题．最后给出了该问题的遗传算法解决方法和计算示例．     

基于定位辅助按需拓扑维护的超宽带自组网路由算法

提出了一种基于定位辅助按需拓扑维护的超宽带自组网路由算法,该算法利用超宽带技术精确定位信息所获得的网络拓扑信息和路由信息进行分组转发,路由维护阶段在定位信息辅助下采用按需方式进行断链路由的修复和拓扑维护,通过基于位置信息的按需路由发现和限制路由查找范围,以及定位信息和网络拓扑信息的及时更新,在降低协议开销的同时保证了算法的有效性。仿真表明,该算法在分组丢失率、平均端到端时延和路由附加开销等方面具有良好性能,其优良的分布式控制特征能适应超宽带自组网的动态环境。     

Improving Convergence of the HastingsMetropolis Algorithm with an Adaptive Proposal

The HastingsMetropolis algorithm is a general MCMC method for sampling from a density known up to a constant. Geometric convergence of this algorithm has been proved under conditions relative to the instrumental (or proposal) distribution. We present an inhomogeneous HastingsMetropolis algorithm for which the proposal density approximates the target density, as the number of iterations increases. The proposal density at the n th step is a non-parametric estimate of the density of the algorithm, and uses an increasing number of i.i.d. copies of the Markov chain. The resulting algorithm converges (in n ) geometrically faster than a HastingsMetropolis algorithm with any fixed proposal distribution. The case of a strictly positive density with compact support is presented first, then an extension to more general densities is given. We conclude by proposing a practical way of implementation for the algorithm, and illustrate it over simulated examples.