An extended space approach for particle Markov chain Monte Carlo methods

In this paper we consider fully Bayesian inference in general state space models. Existing particle Markov chain Monte Carlo (MCMC) algorithms use an augmented model that takes into account all the variable sampled in a sequential Monte Carlo algorithm. This paper describes an approach that also uses sequential Monte Carlo to construct an approximation to the state space, but generates extra states using MCMC runs at each time point. We construct an augmented model for our extended space with the marginal distribution of the sampled states matching the posterior distribution of the state vector. We show how our method may be combined with particle independent Metropolis-Hastings or particle Gibbs steps to obtain a smoothing algorithm. All the Metropolis acceptance probabilities are identical to those obtained in existing approaches, so there is no extra cost in term of Metropolis-Hastings rejections when using our approach. The number of MCMC iterates at each time point is chosen by the used and our augmented model collapses back to the model in Olsson and Ryden (2011) when the number of MCMC iterations reduces. We show empirically that our approach works well on applied examples and can outperform existing methods.Comment: 35 pages, 2 figures, Typos corrected from Version

Bayesian Covariance Matrix Estimation using a Mixture of Decomposable Graphical Models

Estimating a covariance matrix efficiently and discovering its structure are important statistical problems with applications in many fields. This article takes a Bayesian approach to estimate the covariance matrix of Gaussian data. We use ideas from Gaussian graphical models and model selection to construct a prior for the covariance matrix that is a mixture over all decomposable graphs, where a graph means the configuration of nonzero offdiagonal elements in the inverse of the covariance matrix. Our prior for the covariance matrix is such that the probability of each graph size is specified by the user and graphs of equal size are assigned equal probability. Most previous approaches assume that all graphs are equally probable. We give empirical results that show the prior that assigns equal probability over graph sizes outperforms the prior that assigns equal probability over all graphs, both in identifying the correct decomposable graph and in more efficiently estimating the covariance matrix. The advantage is greatest when the number of observations is small relative to the dimension of the covariance matrix. The article also shows empirically that there is minimal change in statistical efficiency in using the mixture over decomposable graphs prior for estimating a general covariance compared to the Bayesian estimator by Wong et al. (2003), even when the graph of the covariance matrix is nondecomposable. However, our approach has some important advantages over that of Wong et al. (2003). Our method requires the number of decomposable graphs for each graph size. We show how to estimate these numbers using simulation and that the simulation results agree with analytic results when such results are known. We also show how to estimate the posterior distribution of the covariance matrix using Markov chain Monte Carlo with the elements of the covariance matrix integrated out and give empirical results that show the sampler is computationally efficient and converges rapidly. Finally, we note that both the prior and the simulation method to evaluate the prior apply generally to any decomposable graphical model.Covariance selection; Graphical models; Reduced conditional sampling; Variable selection

Water availability and agricultural demand:An assessment framework using global datasets in a data scarce catchment, Rokel-Seli River, Sierra Leone

Study region: The proposed assessment framework is aimed at application in Sub-Saharan Africa, but could also be applied in other hydrologically data scarce regions. The test study site was the Rokel-Seli River catchment, Sierra Leone, West Africa. Study focus: We propose a simple, transferable water assessment framework that allows the use of global climate datasets in the assessment of water availability and crop demand in data scarce catchments. In this study, we apply the assessment framework to the catchment of the Rokel-Seli River in Sierra Leone to investigate the capabilities of global datasets complemented with limited historical data in estimating water resources of a river basin facing rising demands from large scale agricultural water withdrawals. We demonstrate how short term river flow records can be extended using a lumped hydrological model, and then use a crop water demand model to generate irrigation water demands for a large irrigated biofuels scheme abstracting from the river. The results of using several different global datasets to drive the assessment framework are compared and the performance evaluated against observed rain and flow gauge records. New hydrological insights: We find that the hydrological model capably simulates both low and high flows satisfactorily, and that all the input datasets consistently produce similar results for water withdrawal scenarios. The proposed framework is successfully applied to assess the variability of flows available for abstraction against agricultural demand. The assessment framework conclusions are robust despite the different input datasets and calibration scenarios tested, and can be extended to include other global input datasets

Using Crowdsourcing to Examine Relations Between Delay and Probability Discounting

This is the author's accepted manuscript. The original is available at http://www.sciencedirect.com/science/article/pii/S0376635712001891Although the extensive lines of research on delay and/or probability discounting have greatly expanded our understanding of human decision-making processes, the relation between these two phenomena remains unclear. For example, some studies have reported robust associations between delay and probability discounting, whereas others have failed to demonstrate a consistent relation between the two. The current study sought to clarify this relation by examining the relation between delay and probability discounting in a large sample of internet users (n= 904) using the Amazon Mechanical Turk (AMT) crowdsourcing service. Because AMT is a novel data collection platform, the findings were validated through the replication of a number of previously established relations (e.g., relations between delay discounting and cigarette smoking status). A small but highly significant positive correlation between delay and probability discounting rates was obtained, and principal component analysis suggested that two (rather than one) components were preferable to account for the variance in both delay and probability discounting. Taken together, these findings suggest that delay and probability discounting may be related, but are not manifestations of a single component (e.g., impulsivity)

Core Health Outcomes In Childhood Epilepsy (CHOICE):Protocol for the selection of a core outcome set

This is the final version of the article. Available from BioMed Central via the DOI in this record.BACKGROUND: There is increasing recognition that establishing a core set of outcomes to be evaluated and reported in trials of interventions for particular conditions will improve the usefulness of health research. There is no established core outcome set for childhood epilepsy. The aim of this work is to select a core outcome set to be used in evaluative research of interventions for children with rolandic epilepsy, as an exemplar of common childhood epilepsy syndromes. METHODS: First we will identify what outcomes should be measured; then we will decide how to measure those outcomes. We will engage relevant UK charities and health professional societies as partners, and convene advisory panels for young people with epilepsy and parents of children with epilepsy. We will identify candidate outcomes from a search for trials of interventions for childhood epilepsy, statutory guidance and consultation with our advisory panels. Families, charities and health, education and neuropsychology professionals will be invited to participate in a Delphi survey following recommended practices in the development of core outcome sets. Participants will be able to recommend additional outcome domains. Over three rounds of Delphi survey participants will rate the importance of candidate outcome domains and state the rationale for their decisions. Over the three rounds we will seek consensus across and between families and health professionals on the more important outcomes. A face-to-face meeting will be convened to ratify the core outcome set. We will then review and recommend ways to measure the shortlisted outcomes using clinical assessment and/or patient-reported outcome measures. DISCUSSION: Our methodology is a proportionate and pragmatic approach to expediently produce a core outcome set for evaluative research of interventions aiming to improve the health of children with epilepsy. A number of decisions have to be made when designing a study to develop a core outcome set including defining the scope, choosing which stakeholders to engage, most effective ways to elicit their views, especially children and a potential role for qualitative research.This study is part of Changing Agendas on Sleep, Treatment and Learning in Childhood Epilepsy (CASTLE), which is funded by the National Institute for Health Research (NIHR) Programme Grants for Applied Research RP-PG-0615-20007

The Transit Light Curve Project. XIII. Sixteen Transits of the Super-Earth GJ 1214b

We present optical photometry of 16 transits of the super-Earth GJ 1214b, allowing us to refine the system parameters and search for additional planets via transit timing. Starspot-crossing events are detected in two light curves, and the star is found to be variable by a few percent. Hence, in our analysis, special attention is given to systematic errors that result from star spots. The planet-to-star radius ratio is 0.11610+/-0.00048, subject to a possible upward bias by a few percent due to the unknown spot coverage. Even assuming this bias to be negligible, the mean density of planet can be either 3.03+/-0.50 g cm^{-3} or 1.89+/-0.33 g cm^{-3}, depending on whether the stellar radius is estimated from evolutionary models or from an empirical mass-luminosity relation combined with the light curve parameters. One possible resolution is that the orbit is eccentric (e approximately equal to 0.14), which would favor the higher density, and hence a much thinner atmosphere for the planet. The transit times were found to be periodic within about 15s, ruling out the existence of any other super-Earths with periods within a factor-of-two of the known planet.Comment: Accepted in Ap

Cues and knowledge structures used by mental-health professionals when making risk assessments

Background: Research into mental-health risks has tended to focus on epidemiological approaches and to consider pieces of evidence in isolation. Less is known about the particular factors and their patterns of occurrence that influence clinicians’ risk judgements in practice. Aims: To identify the cues used by clinicians to make risk judgements and to explore how these combine within clinicians’ psychological representations of suicide, self-harm, self-neglect, and harm to others. Method: Content analysis was applied to semi-structured interviews conducted with 46 practitioners from various mental-health disciplines, using mind maps to represent the hierarchical relationships of data and concepts. Results: Strong consensus between experts meant their knowledge could be integrated into a single hierarchical structure for each risk. This revealed contrasting emphases between data and concepts underpinning risks, including: reflection and forethought for suicide; motivation for self-harm; situation and context for harm to others; and current presentation for self-neglect. Conclusions: Analysis of experts’ risk-assessment knowledge identified influential cues and their relationships to risks. It can inform development of valid risk-screening decision support systems that combine actuarial evidence with clinical expertise

Risk factors associated with the epilepsy treatment gap in Kilifi, Kenya: a cross-sectional study.

BACKGROUND: Many people with epilepsy in low-income countries do not receive appropriate biomedical treatment. This epilepsy treatment gap might be caused by patients not seeking biomedical treatment or not adhering to prescribed antiepileptic drugs (AEDs). We measured the prevalence of and investigated risk factors for the epilepsy treatment gap in rural Kenya. METHODS: All people with active convulsive epilepsy identified during a cross-sectional survey of 232,176 people in Kilifi were approached. The epilepsy treatment gap was defined as the percentage of people with active epilepsy who had not accessed biomedical services or who were not on treatment or were on inadequate treatment. Information about risk factors was obtained through a questionnaire-based interview of sociodemographic characteristics, socioeconomic status, access to health facilities, seizures, stigma, and beliefs and attitudes about epilepsy. The factors associated with people not seeking biomedical treatment and not adhering to AEDs were investigated separately, adjusted for age. FINDINGS: 673 people with epilepsy were interviewed, of whom 499 (74%) reported seeking treatment from a health facility. Blood samples were taken from 502 (75%) people, of whom 132 (26%) reported taking AEDs, but 189 (38%) had AEDs detectable in the blood. The sensitivity and specificity of self-reported adherence compared with AEDs detected in blood were 38·1% (95% CI 31·1-45·4) and 80·8% (76·0-85·0). The epilepsy treatment gap was 62·4% (58·1-66·6). In multivariable analysis, failure to seek biomedical treatment was associated with a patient holding traditional animistic religious beliefs (adjusted odds ratio 1·85, 95% CI 1·11-2·71), reporting negative attitudes about biomedical treatment (0·86, 0·78-0·95), living more than 30 km from health facilities (3·89, 1·77-8·51), paying for AEDs (2·99, 1·82-4·92), having learning difficulties (2·30, 1·29-4·11), having had epilepsy for longer than 10 years (4·60, 2·07-10·23), and having focal seizures (2·28, 1·50-3·47). Reduced adherence was associated with negative attitudes about epilepsy (1·10, 1·03-1·18) and taking of AEDs for longer than 5 years (3·78, 1·79-7·98). INTERPRETATION: The sensitivity and specificity of self-reported adherence is poor, but on the basis of AED detection in blood almost two-thirds of patients with epilepsy were not on treatment. Education about epilepsy and making AEDs freely available in health facilities near people with epilepsy should be investigated as potential ways to reduce the epilepsy treatment gap. FUNDING: Wellcome Trust