On the flexibility of the design of Multiple Try Metropolis schemes

The Multiple Try Metropolis (MTM) method is a generalization of the classical Metropolis-Hastings algorithm in which the next state of the chain is chosen among a set of samples, according to normalized weights. In the literature, several extensions have been proposed. In this work, we show and remark upon the flexibility of the design of MTM-type methods, fulfilling the detailed balance condition. We discuss several possibilities and show different numerical results

Metropolis Sampling

Monte Carlo (MC) sampling methods are widely applied in Bayesian inference, system simulation and optimization problems. The Markov Chain Monte Carlo (MCMC) algorithms are a well-known class of MC methods which generate a Markov chain with the desired invariant distribution. In this document, we focus on the Metropolis-Hastings (MH) sampler, which can be considered as the atom of the MCMC techniques, introducing the basic notions and different properties. We describe in details all the elements involved in the MH algorithm and the most relevant variants. Several improvements and recent extensions proposed in the literature are also briefly discussed, providing a quick but exhaustive overview of the current Metropolis-based sampling's world.Comment: Wiley StatsRef-Statistics Reference Online, 201

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