Bayesian MCMC Mapping of Quantitative Trait Loci in a Half-sib Design: a Graphical Model Perspective

Graphical models provide a powerful and flexible approach to the analysis of complex problems in genetics. While task-specific software may be extremely efficient for any particular analysis, it is often difficult to adapt to new computational challenges. By viewing these genetic applications in a more general framework, many problems can be handled by essentially the same software. This is advantageous in an area where fast methodological development is essential. Once a method has been fully developed and tested, problem-specific software may then be required. The aim of this paper is to illustrate the potential use of a graphical model approach to genetic analyses by taking a very simple and well-understood problem by way of example.     

Testing equality of variances in the analysis of repeated measurements

The problem of comparing the precisions of two instruments using repeated measurements can be cast as an extension of the Pitman-Morgan problem of testing equality of variances of a bivariate normal distribution. Hawkins (1981) decomposes the hypothesis of equal variances in this model into two subhypotheses for which simple tests exist. For the overall hypothesis he proposes to combine the tests of the subhypotheses using Fisher's method and empirically compares the component tests and their combination with the likelihood ratio test. In this paper an attempt is made to resolve some discrepancies and puzzling conclusions in Hawkins's study and to propose simple modifications.
The new tests are compared to the tests discussed by Hawkins and to each other both in terms of the finite sample power (estimated by Monte Carlo simulation) and theoretically in terms of asymptotic relative efficiencies.     

Exact confidence sets and goodness-of-fit methods for stable distributions

Usual inference methods for stable distributions are typically based on limit distributions. But asymptotic approximations can easily be unreliable in such cases, for standard regularity conditions may not apply or may hold only weakly. This paper proposes finite-sample tests and confidence sets for tail thickness and asymmetry parameters (α$\alpha$ and β$\beta$) of stable distributions. The confidence sets are built by inverting exact goodness-of-fit tests for hypotheses which assign specific values to these parameters. We propose extensions of the Kolmogorov–Smirnov, Shapiro–Wilk and Filliben criteria, as well as the quantile-based statistics proposed by McCulloch (1986) in order to better capture tail behavior. The suggested criteria compare empirical goodness-of-fit or quantile-based measures with their hypothesized values. Since the distributions involved are quite complex and non-standard, the relevant hypothetical measures are approximated by simulation, and p$p$-values are obtained using Monte Carlo (MC) test techniques. The properties of the proposed procedures are investigated by simulation. In contrast with conventional wisdom, we find reliable results with sample sizes as small as 25. The proposed methodology is applied to daily electricity price data in the US over the period 2001–2006. The results show clearly that heavy kurtosis and asymmetry are prevalent in these series.     

随机数在随机事件与概率教学中的应用探索

本文对在随机事件与概率中的常见问题提出了一种新的借助于计算机实现的解决思路,即通过机器自动产生随机数后构建相应的数学模型,再通过编程计算得到最后结果。该方法既为概率论的教学带来了创新性思维,也为当前的教师提出了新的挑战。     

On the cost of delayed currency fixing announcements

In Foreign Exchange Markets vanilla and barrier options are traded frequently. The market standard is a cutoff time of 10:00 a.m. in New York for the strike of vanillas and a knock-out event based on a continuously observed barrier in the inter bank market. However, many clients, particularly from Italy, prefer the cutoff and knock-out event to be based on the fixing published by the European Central Bank on the Reuters Page ECB37. These barrier options are called discretely monitored barrier options. While these options can be priced in several models by various techniques, the ECB source of the fixing causes two problems. First of all, it is not tradable, and secondly it is published with a delay of about 10–20 min. We examine here the effect of these problems on the hedge of those options and consequently suggest a cost based on the additional uncertainty encountered.      

房地产开发企业违约概率压力测试研究——现金流蒙特卡洛模拟方法在银行中的应用

本文采用蒙特卡洛模拟方法,根据现金净额是否为负这一标准来判断房地产开发企业是否违约,在对企业的现金流进行随机模拟的基础上来计算企业的违约概率。压力测试的场景为房价下降,利率上升。压力传导途径为房价与利率变动导致企业销售收入变动,销售收入的改变导致企业的现金流量表发生变化。房价和利率对销售收入的冲击是随机的,企业的现金流也是随机的,本文通过随机模拟估算了企业的现金流为负的频率,以此作为企业违约的概率。压力测试表明,当房价下降幅度到达15%附近时,房地产开发商的违约概率开始急剧上升。