Geometric ergodicity of the Random Walk Metropolis with position-dependent proposal covariance

We consider a Metropolis-Hastings method with proposal kernel $\mathcal{N}(x,hG^{-1}(x))$, where $x$ is the current state. After discussing specific cases from the literature, we analyse the ergodicity properties of the resulting Markov chains. In one dimension we find that suitable choice of $G^{-1}(x)$ can change the ergodicity properties compared to the Random Walk Metropolis case $\mathcal{N}(x,h\Sigma)$, either for the better or worse. In higher dimensions we use a specific example to show that judicious choice of $G^{-1}(x)$ can produce a chain which will converge at a geometric rate to its limiting distribution when probability concentrates on an ever narrower ridge as $|x|$ grows, something which is not true for the Random Walk Metropolis.Comment: 15 pages + appendices, 4 figure

Ken Livingstone: “Londoners need a city where they can make their home, feel safe and not be priced out”

Labour candidate for the London Mayor Ken Livingstone discusses his plans to introduce a London-wide education maintenance allowance, campaign for a London ‘Living Rent’ and to resign within six months if he has not achieved his goals to cut public transport costs. This is the second in a three part series with the mayoral candidates, including Brian Paddick and Jenny Jones, with an introduction by Tony Travers

Improving the quality of assessment and management of hypoglycaemia in hospitalised patients with diabetes mellitus by introducing 'hypo boxes' to general medical wards with a specialist interest in diabetes

Diabetes is becoming more prevalent in the UK and this is represented in the in-patient cohort, such that 1 in 6 hospital patients have diabetes (1). The UK National Diabetes In-Patient Audit in 2012 estimated that 30% of patients experience one episode of hypoglycaemia during admission. Hypoglycaemia is associated with increased morbidity and mortality, and longer length of hospital stay. It is therefore important that hypoglycaemia is managed promptly and effectively to reduce associated morbidity. The Joint British Diabetes Society recommends that all wards should have access to ‘Hypo Boxes’ (2). We assessed all episodes of hypoglycaemia (<4.0 mmol/l) in the diabetes wards in over a 4 week period. ‘Hypo Boxes’ were installed to the wards and the appropriateness of treatment and time to correction of hypoglycaemia was re-assessed. Assessment of hypoglycaemia pre-intervention revealed 45 episodes of hypoglycaemia in 14 patients, and 42% (n=19) of episodes were deemed to have been treated appropriately. Only 17.8% of episodes were corrected within 30 minutes, and 33.3% were corrected within 60 minutes. A third of patients (35%) did not have a further blood glucose checked. Following intervention, there was a marked improvement in management. The proportion of appropriately managed episodes increased to 82% (n=35) and management of episodes of severe hypoglycaemia (<3.0 mmol/l) increased to 94%. The time to correction increased with 40% of episodes corrected to >4.0 mmol/l within 30 minutes, and a further 54% between 30-60 minutes. In conclusion, the introduction of ‘Hypo Boxes’ improved the assessment and management of hypoglycaemia

Information-geometric Markov Chain Monte Carlo methods using Diffusions

Recent work incorporating geometric ideas in Markov chain Monte Carlo is reviewed in order to highlight these advances and their possible application in a range of domains beyond Statistics. A full exposition of Markov chains and their use in Monte Carlo simulation for Statistical inference and molecular dynamics is provided, with particular emphasis on methods based on Langevin diffusions. After this geometric concepts in Markov chain Monte Carlo are introduced. A full derivation of the Langevin diffusion on a Riemannian manifold is given, together with a discussion of appropriate Riemannian metric choice for different problems. A survey of applications is provided, and some open questions are discussed.Comment: 22 pages, 2 figure

Associations between dietary added sugar intake and micronutrient intake: a systematic review

Original article can be found at: http://journals.cambridge.org/ Copyright The Authors. DOI: 10.1017/S0007114507617206There is increasing concern that high intakes of added sugars might compromise intakes of micronutrients. The objectives of this systematic review were (1) to determine whether dietary added sugar intake was associated with micronutrient intakes, and if so, whether there was evidence of micronutrient dilution as a result of higher dietary added sugar intake and (2) if micronutrient dilution was present, to determine whether there was sufficiently robust evidence to support a threshold effect above which there was a significant decline in micronutrient intake or status relative to the recommended intakes. A systematic computerised literature search was undertaken, limited to studies written in English published from 1980 onwards and further studies identified through hand searching papers. Fifteen studies that assessed associations between intakes of added sugars or non-milk extrinsic sugars and micronutrients were included. Overall, there are insufficient data and inconsistency between studies in relationships between added sugars and micronutrient intakes, with no clear evidence of micronutrient dilution or a threshold for a quantitative amount of added sugar intake for any of the micronutrients investigated. The current evidence base is considerably constrained by methodological issues. Further research is required to determine which food products high in added sugars might adversely affect micronutrient intakes by displacing other food items from the diet. Analyses should take into account the magnitude of any observed associations to determine their true biological significance.Peer reviewe

Effective Approaches With Young Adults: A Guide for Probation Services

The aim of this guide is to give probation practitioners, whether in the National Probation Service or Community Rehabilitation Companies, the tools to deliver a more effective approach to young adults. It provides practical suggestions for effective ways to engage young adults and support their desistance from crime. It also includes suggestions for managers on what they can do to enable practitioners to improve outcomes within probation services

Adaptive MBER space-time DFE assisted multiuser detection for SDMA systems

In this contribution we propose a space-time decision feedback equalization (ST-DFE) assisted multiuser detection (MUD) scheme for multiple antenna aided space division multiple access systems. A minimum bit error rate (MBER) design is invoked for the MUD, which is shown to be capable of improving the achievable bit error rate performance over that of the minimum mean square error (MMSE) design. An adaptive MBER ST-DFE-MUD is proposed using the least bit error rate algorithm, which is demonstrated to consistently outperform the least mean square (LMS) algorithm, while achieving a lower computational complexity than the LMS algorithm for the binary signalling scheme. Simulation results demonstrate that theMBER ST-DFE-MUD is more robust to channel estimation errors as well as to error propagation imposed by decision feedback errors, compared to the MMSE ST-DFE-MUD