CLTs and asymptotic variance of time-sampled Markov chains

For a Markov transition kernel P and a probability distribution μ on nonnegative integers, a time-sampled Markov chain evolves according to the transition kernel Pμ = Σkμ(k)Pk. In this note we obtain CLT conditions for time-sampled Markov chains and derive a spectral formula for the asymptotic variance. Using these results we compare efficiency of Barker's and Metropolis algorithms in terms of asymptotic variance

The UK clinical aptitude test and clinical course performance at Nottingham: a prospective cohort study

Background The UK Clinical Aptitude Test (UKCAT) was introduced in 2006 as an additional tool for the selection of medical students. It tests mental ability in four distinct domains (Verbal Reasoning, Quantitative Reasoning, Abstract Reasoning, and Decision Analysis), and the results are available to students and admission panels in advance of the selection process. Our first study showed little evidence of any predictive validity for performance in the first two years of the Nottingham undergraduate course. The study objective was to determine whether the UKCAT scores had any predictive value for the later parts of the course, largely delivered via clinical placements. Methods Students entering the course in 2007 and who had taken the UKCAT were asked for permission to use their anonymised data in research. The UKCAT scores were incorporated into a database with routine pre-admission socio-demographics and subsequent course performance data. Correlation analysis was followed by hierarchical multivariate linear regression. Results The original study group comprised 204/254 (80%) of the full entry cohort. With attrition over the five years of the course this fell to 185 (73%) by Year 5. The Verbal Reasoning score and the UKCAT Total score both demonstrated some univariate correlations with clinical knowledge marks, and slightly less with clinical skills. No parts of the UKCAT proved to be an independent predictor of clinical course marks, whereas prior attainment was a highly significant predictor (p <0.001). Conclusions This study of one cohort of Nottingham medical students showed that UKCAT scores at admission did not independently predict subsequent performance on the course. Whilst the test adds another dimension to the selection process, its fairness and validity in selecting promising students remains unproven, and requires wider investigation and debate by other schools

Approximate confidence intervals for a linear combination of binomial proportions: A new variant

We propose a new adjustment for constructing an improved version of theWald interval for linear combinations of binomial proportions, which addresses the presence of extremal samples. A comparative simulation study was carried out to investigate the performance of this new variant with respect to the exact coverage probability, expected interval length, and mesial and distal noncoverage probabilities. Additionally, we discuss the application of a criterion for interpreting interval location in the case of small samples and/or in situations in which extremal observations exist. The confidence intervals obtained from the new variant performed better for some evaluation measures