蒙特卡罗方法在核类本科专业的教学初探

蒙特卡罗方法是以概率统计理论为基础、通过计算机编程而实现的一种数值计算方法,在核科学与技术等领域有着广泛的应用。新时期下,初步尝试面向核类本科专业开设蒙特卡罗方法这门课程,将概率统计思想和编程实践训练融入到蒙特卡罗方法教学中,教学取得了一定成效。     

A direct Monte Carlo approach for Bayesian analysis of the seemingly unrelated regression model

Computationally efficient methods for Bayesian analysis of seemingly unrelated regression (SUR) models are described and applied that involve the use of a direct Monte Carlo (DMC) approach to calculate Bayesian estimation and prediction results using diffuse or informative priors. This DMC approach is employed to compute Bayesian marginal posterior densities, moments, intervals and other quantities, using data simulated from known models and also using data from an empirical example involving firms’ sales. The results obtained by the DMC approach are compared to those yielded by the use of a Markov Chain Monte Carlo (MCMC) approach. It is concluded from these comparisons that the DMC approach is worthwhile and applicable to many SUR and other problems.     

On the Application of Markov Chain Monte Carlo Methods to Genetic Analyses on Complex Pedigrees

Markov chain Monte Carlo methods are frequently used in the analyses of genetic data on pedigrees for the estimation of probabilities and likelihoods which cannot be calculated by existing exact methods. In the case of discrete data, the underlying Markov chain may be reducible and care must be taken to ensure that reliable estimates are obtained. Potential reducibility thus has implications for the analysis of the mixed inheritance model, for example, where genetic variation is assumed to be due to one single locus of large effect and many loci each with a small effect. Similarly, reducibility arises in the detection of quantitative trait loci from incomplete discrete marker data. This paper aims to describe the estimation problem in terms of simple discrete genetic models and the single-site Gibbs sampler. Reducibility of the Gibbs sampler is discussed and some current methods for circumventing the problem outlined.     

Assessing the Behaviour of Non-Survey Methods for Constructing Regional Input–Output Tables through a Monte Carlo Simulation

The paper aims to analyse the behaviour of a battery of non-survey techniques of constructing regional I-O tables in estimating impact. For this aim, a Monte Carlo simulation, based on the generation of ‘true’ multiregional I-O tables, was carried out. By aggregating multi-regional I-O tables, national I-O tables were obtained. From the latter, indirect regional tables were derived through the application of various regionalisation methods and the relevant multipliers were compared with the ‘true’ multipliers using a set of statistics. Three aspects of the behaviour of the methods have been analysed: performances to reproduce ‘true’ multipliers, variability of simulation error and direction of bias. The results have demonstrated that the Flegg et al. Location Quotient (FLQ) and its augmented version (AFLQ) represent an effective improvement of conventional techniques based on the use of location quotients in both reproducing ‘true’ multipliers and generating more stable simulation errors. In addition, the results have confirmed the existence of a tendency of the methods to over/underestimate impact. In the cases of the FLQ and the AFLQ, this tendency depends on the value of the parameter δ.