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.     

Sharp tongues and bitter pills

How bad is big pharma? An American medical journal has taken draconian measures to vet analyses of clinical trials sponsored by the pharmaceutical industry. Are their statistics so bad? Stephen Senn has a look at the controversy.     

Comparing Estimates of the Effects of Air Pollution on Human Mortality Obtained Using Different Regression Methodologies

Studies using regression techniques report their results using a variety of statistics. Evaluation of the consistency of findings, such as in a metaanalysis, requires calculating the statistical estimates of the effect reported in each study in a comparable manner. In this paper, we consider multiple linear regression, multiple Poisson regression, and logistic regression estimates. We present results that are needed to calculate, on a common basis, the slope of the regression function at a specified value, the elasticity function of the regression function at a specified value, the relative risk at a specified value, and the odds ratio at a specified value. We apply these results to studies of the association of daily mortality in an area to the daily air pollution level of ozone and PM₁₀. We calculate the estimated slope of the number of deaths per billion population associated with an increase of 1 ppb of ozone level in studies of daily mortality in three urban areas. These studies, in Los Angeles, New York, and St. Louis, produced very comparable results on a common basis, especially when compared to the coefficients as reported. We also calculated the estimated elasticity function of the daily mortality and daily PM₁₀ level for eight areas and found that the elasticities varied within a factor of roughly two, much less than the variability in the coefficients as reported.     

Development and Consideration of Global Policies for Managing the Future Risks of Poliovirus Outbreaks: Insights and Lessons Learned Through Modeling

The success of the Global Polio Eradication Initiative promises to bring large benefits, including sustained improvements in quality of life (i.e., cases of paralytic disease and deaths avoided) and costs saved from cessation of vaccination. Obtaining and maintaining these benefits requires that policymakers manage the transition from the current massive use of oral poliovirus vaccine (OPV) to a world without OPV and free of the risks of potential future reintroductions of live polioviruses. This article describes the analytical journey that began in 2001 with a retrospective case study on polio risk management and led to development of dynamic integrated risk, economic, and decision analysis tools to inform global policies for managing the risks of polio. This analytical journey has provided several key insights and lessons learned that will be useful to future analysts involved in similar complex decision-making processes.     

Defining contracts between the state and charitable organisations in national accounts: a perspective from the UK

This paper explores the issues inherent in defining contracts for service delivery between the state and charitable organisations, and in differentiating them from grants. It begins by making the point that there is no one correct definition of a contract; rather, it is a function of its purpose. It then details our work in developing a definition of a contract within the national accounting tradition, as part of a study of the contribution of charitable organisations to the GDP of the United Kingdom. The paper ends by drawing some general conclusions from this experience.     

Newcomb's Hidden Regress

Newcomb's problem supposedly involves your choosing one or else two boxes in circumstances in which a predictor has made a prediction of how many boxes you will choose. We argue that the circumstances which allegedly define Newcomb's problem generate a previously unnoticed regress which shows that Newcomb's problem is insoluble because it is ill-formed. Those who favor, as we do, a ``no-box' reply to Newcomb's problem typically claim either that the problem's solution is underdetermined or else that it is overdetermined. We are no-boxers of the first kind, but the underdetermination we identify is more radical than any previously identified: it blocks the very set-up of the problem and not just potential solutions to the problem once it has been set up. The defect is subtle, but it cripples every genuine version of the problem, regardless of variations in such things as the predictor's degree of reliability, the basis on which the prediction is made, or the amount of money in each box. The regress shows that, surprisingly enough, no one can understand Newcomb's problem, and so no one can possibly solve it.     

Enclaves, neighbourhood effects and employment outcomes: Ethnic minorities in England and Wales

Ethnic minorities in England and Wales are spatially concentrated in relatively-deprived urban areas. Both geographic clustering and the economic characteristics of ethnically-concentrated neighbourhoods can impact upon the opportunities and constraints facing residents of such areas. This paper explores the relationship between the existence of enclaves and the employment prospects of ethnic minorities in England and Wales. It is shown that there is considerable spatial variation in employment outcomes. There is a lower incidence of self-employment in more ethnically-concentrated urban areas, which contradicts the view of ethnic entrepreneurship as an enclave phenomenon. Unemployment rates are also higher for minorities living in more concentrated areas. Enclaves in England and Wales do not appear to offer many economic benefits to minority individuals. Received: 31 December 1999/Accepted: 27 November 2000     

Reliance on sources of information for water-saving practices by irrigators in the High Plains of the U.S.A.

Who do farmers trust? Irrigators in the High Plains are confronted with a wide range of information sources with respect to water-saving practices. From a survey of 709 irrigators in 10 countries the most widely accepted sources are identified, regional variability of information is examined, the role of irrigator characteristics on source selection is determined, and the level of association between adoption and source preference is analyzed. Differences in irrigators' reliance on specific sources are more associated with location than irrigator characteristics. Information sources viewed as important by many irrigators frequently influence adoption decisions less than sources having a wide range of preference among irrigators. Mass media and advisor-oriented sources are much more significantly linked to adoption than inter-personal sources such as friends and neighbors. The three sources that best discriminate adoption behavior are private agricultural consulting firms, university research stations, and trade magazines.