Acceleration of the Multiple-Try Metropolis algorithm using antithetic and stratified sampling

The Multiple-Try Metropolis is a recent extension of the Metropolis algorithm in which the next state of the chain is selected among a set of proposals. We propose a modification of the Multiple-Try Metropolis algorithm which allows for the use of correlated proposals, particularly antithetic and stratified proposals. The method is particularly useful for random walk Metropolis in high dimensional spaces and can be used easily when the proposal distribution is Gaussian. We explore the use of quasi Monte Carlo (QMC) methods to generate highly stratified samples. A series of examples is presented to evaluate the potential of the method.     

一种定量敏感性问题的随机化调查方法

在敏感性问题的随机化调查中,既有调查个体是否具有敏感属性的二值敏感性问题,即属性特征问题,又有调查特定人群中敏感指标量的“多少”问题,即定量特征敏感性问题.对于定量特征敏感性问题的调查,E ichhorn,H aryre于1983年提出了一种随机化调查方法,并给出了定量敏感问题指标量均值的一个无偏估计.本文提出一种定量特征敏感性问题的随机化调查方法,得到的结果表明,本文提出的方法优于E ichhorn,H aryre(1983)提出的方法.     

Issues Related to Sports Gambling

This paper looks at various issues that are of interest to the sports gambler. First, an expression is obtained for the distribution of the final bankroll using fixed wagers with a specified initial bankroll. Second, fixed percentage wagers are considered where the Kelly method is extended to the case of simultaneous bets placed at various odds; a computational algorithm is presented to obtain the Kelly fractions. Finally, the paper considers the problem of determining whether a gambling system is profitable based on the historical results of bets placed at various odds.     

宽带LFM信号去斜率数字脉压方法性能分析

在宽带LFM信号数字脉压中,去斜率数字脉压方法能有效地降低采样率,但是受到目标回波信号与参考信号的时延差的限制,只能作局部脉压处理。同时目标回波信号与参考信号的时延差和目标多普勒频率的变化,对去斜率数字脉压结果有一定的影响。该文通过理论分析和较全面的仿真,定量地分析了去斜率数字脉压中目标回波信号与参考信号时延差和多普勒频率的变化对数字脉压性能的影响,为工程应用中合理选择信号带宽、采样率和目标回波信号的时延提供了参考。     

Using a mixture model for multiple imputation in the presence of outliers: the 'Healthy for life' project

Summary.  We consider the problem of obtaining population-based inference in the presence of missing data and outliers in the context of estimating the prevalence of obesity and body mass index measures from the 'Healthy for life' study. Identifying multiple outliers in a multivariate setting is problematic because of problems such as masking, in which groups of outliers inflate the covariance matrix in a fashion that prevents their identification when included, and swamping, in which outliers skew covariances in a fashion that makes non-outlying observations appear to be outliers. We develop a latent class model that assumes that each observation belongs to one of K unobserved latent classes, with each latent class having a distinct covariance matrix. We consider the latent class covariance matrix with the largest determinant to form an 'outlier class'. By separating the covariance matrix for the outliers from the covariance matrices for the remainder of the data, we avoid the problems of masking and swamping. As did Ghosh-Dastidar and Schafer, we use a multiple-imputation approach, which allows us simultaneously to conduct inference after removing cases that appear to be outliers and to promulgate uncertainty in the outlier status through the model inference. We extend the work of Ghosh-Dastidar and Schafer by embedding the outlier class in a larger mixture model, consider penalized likelihood and posterior predictive distributions to assess model choice and model fit, and develop the model in a fashion to account for the complex sample design. We also consider the repeated sampling properties of the multiple imputation removal of outliers.     

Markov Chain Monte Carlo in small worlds

As the number of applications for Markov Chain Monte Carlo (MCMC) grows, the power of these methods as well as their shortcomings become more apparent. While MCMC yields an almost automatic way to sample a space according to some distribution, its implementations often fall short of this task as they may lead to chains which converge too slowly or get trapped within one mode of a multi-modal space. Moreover, it may be difficult to determine if a chain is only sampling a certain area of the space or if it has indeed reached stationarity. In this paper, we show how a simple modification of the proposal mechanism results in faster convergence of the chain and helps to circumvent the problems described above. This mechanism, which is based on an idea from the field of “small-world” networks, amounts to adding occasional “wild” proposals to any local proposal scheme. We demonstrate through both theory and extensive simulations, that these new proposal distributions can greatly outperform the traditional local proposals when it comes to exploring complex heterogenous spaces and multi-modal distributions. Our method can easily be applied to most, if not all, problems involving MCMC and unlike many other remedies which improve the performance of MCMC it preserves the simplicity of the underlying algorithm.     

BAYESIAN HIDDEN MARKOV MODELS FOR LONGITUDINAL COUNTS

This paper describes a Bayesian approach to modelling carcinogenity in animal studies where the data consist of counts of the number of tumours present over time. It compares two autoregressive hidden Markov models. One of them models the transitions between three latent states: an inactive transient state, a multiplying state for increasing counts and a reducing state for decreasing counts. The second model introduces a fourth tied state to describe non‐zero observations that are neither increasing nor decreasing. Both these models can model the length of stay upon entry of a state. A discrete constant hazards waiting time distribution is used to model the time to onset of tumour growth. Our models describe between‐animal‐variability by a single hierarchy of random effects and the within‐animal variation by first‐order serial dependence. They can be extended to higher‐order serial dependence and multi‐level hierarchies. Analysis of data from animal experiments comparing the influence of two genes leads to conclusions that differ from those of Dunson (2000). The observed data likelihood defines an information criterion to assess the predictive properties of the three‐ and four‐state models. The deviance information criterion is appropriately defined for discrete parameters.     

Age at first marriage in Malawi: a Bayesian multilevel analysis using a discrete time-to-event model

Summary.  The paper presents a hierarchical discrete time survival model for the analysis of the 2000 Malawi Demographic and Health Survey data to assess the determinants of transition to marriage among women in Malawi. The model explicitly accounts for the unobserved heterogeneity by using family and community random effects with cross-level correlation structure. A nonparametric technique is used to model the base-line discrete hazard dynamically. Parameters of the model are computed by using a Markov chain Monte Carlo algorithm. The results show that rising age at marriage is a combination of birth cohort and education effects, depends considerably on the family and to some extent on the community in which a woman resides and the correlation between family and community random effects is negative. These results confirm a downward trend in teenage marriage and that raising women's education levels in sub-Saharan Africa has the beneficial effect of increasing age at marriage, and by implication reducing total fertility rates. The negative correlation between family and community random effects has policy implications in that targeting communities with an intervention to increase age at first marriage may not necessarily yield reduced fertility levels in individual families. A campaign that is geared towards individual families would achieve the desired goals. Overall, the findings point to the need for the Government in Malawi to enact public policies which are geared at vastly improving women's education at higher levels. The variation in marriage rates over families poses problems in delivering the policy, since particular policies must be devised for specific groups of families to accomplish the required social and health objectives.     

Design priorities and disciplinary perspectives: the case of the US National Children's Study

Summary.  The National Children's Study (NCS), which was undertaken in 2000 by collaboration between several US federal government agencies, is one of the largest and boldest longitudinal studies of children's health ever undertaken. One of the key design issues has been the nature of the NCS sample. The paper describes the nature of the choices and the reasons for the decision that the NCS be based on a national probability sample. Designed as a study of the environmental influences on children's health and development, the NCS is expected to identify, enrol and follow about 100000 children from their birth to the age of 21 years. A broad definition of relevant environments of interest, and a full partnership between government, university and medical scientists, introduces considerable challenges in the design of the study.