Multimodal nested sampling: an efficient and robust alternative to MCMC methods for astronomical data analysis

In performing a Bayesian analysis of astronomical data, two difficult problems often emerge. First, in estimating the parameters of some model for the data, the resulting posterior distribution may be multimodal or exhibit pronounced (curving) degeneracies, which can cause problems for traditional MCMC sampling methods. Second, in selecting between a set of competing models, calculation of the Bayesian evidence for each model is computationally expensive. The nested sampling method introduced by Skilling (2004), has greatly reduced the computational expense of calculating evidences and also produces posterior inferences as a by-product. This method has been applied successfully in cosmological applications by Mukherjee et al. (2006), but their implementation was efficient only for unimodal distributions without pronounced degeneracies. Shaw et al. (2007), recently introduced a clustered nested sampling method which is significantly more efficient in sampling from multimodal posteriors and also determines the expectation and variance of the final evidence from a single run of the algorithm, hence providing a further increase in efficiency. In this paper, we build on the work of Shaw et al. and present three new methods for sampling and evidence evaluation from distributions that may contain multiple modes and significant degeneracies; we also present an even more efficient technique for estimating the uncertainty on the evaluated evidence. These methods lead to a further substantial improvement in sampling efficiency and robustness, and are applied to toy problems to demonstrate the accuracy and economy of the evidence calculation and parameter estimation. Finally, we discuss the use of these methods in performing Bayesian object detection in astronomical datasets.Comment: 14 pages, 11 figures, submitted to MNRAS, some major additions to the previous version in response to the referee's comment

Inhibition of the \u3cem\u3edapE\u3c/em\u3e-Encoded \u3cem\u3eN\u3c/em\u3e-Succinyl- ʟ, ʟ-diaminopimelic Acid Desuccinylase from \u3cem\u3eNeisseria meningitidis\u3c/em\u3e by ʟ-Captopril

Binding of the competitive inhibitor ʟ-captopril to the dapE-encoded N-succinyl-ʟ, ʟ-diaminopimelic acid desuccinylase from Neisseria meningitidis (NmDapE) was examined by kinetic, spectroscopic, and crystallographic methods. ʟ-Captopril, an angiotensin-converting enzyme (ACE) inhibitor, was previously shown to be a potent inhibitor of the DapE from Haemophilus influenzae (HiDapE) with an IC50 of 3.3 μM and a measured Ki of 1.8 μM and displayed a dose-responsive antibiotic activity toward Escherichia coli. ʟ-Captopril is also a competitive inhibitor of NmDapE with a Ki of 2.8 μM. To examine the nature of the interaction of ʟ-captopril with the dinuclear active site of DapE, we have obtained electron paramagnetic resonance (EPR) and magnetic circular dichroism (MCD) data for the enzymatically hyperactive Co(II)-substituted forms of both HiDapE and NmDapE. EPR and MCD data indicate that the two Co(II) ions in DapE are antiferromagnetically coupled, yielding an S = 0 ground state, and suggest a thiolate bridge between the two metal ions. Verification of a thiolate-bridged dinuclear complex was obtained by determining the three-dimensional X-ray crystal structure of NmDapE in complex with ʟ-captopril at 1.8 Å resolution. Combination of these data provides new insights into binding of ʟ-captopril to the active site of DapE enzymes as well as important inhibitor–active site residue interaction’s. Such information is critical for the design of new, potent inhibitors of DapE enzymes

Exploring differences in adverse symptom event grading thresholds between clinicians and patients in the clinical trial setting

Symptomatic adverse event (AE) monitoring is essential in cancer clinical trials to assess patient safety, as well as inform decisions related to treatment and continued trial participation. As prior research has demonstrated that conventional concordance metrics (e.g., intraclass correlation) may not capture nuanced aspects of the association between clinician and patient-graded AEs, we aimed to characterize differences in AE grading thresholds between doctors (MDs), registered nurses (RNs), and patients using the Bayesian Graded Item Response Model (GRM)

Efficient Bayesian inference for multimodal problems in cosmology

Bayesian model selection provides the cosmologist with an exacting tool to distinguish between competing models based purely on the data, via the Bayesian evidence. Previous methods to calculate this quantity either lacked general applicability or were computationally demanding. However, nested sampling (Skilling 2004), which was recently applied successfully to cosmology by Muhkerjee et al. 2006, overcomes both of these impediments. Their implementation restricts the parameter space sampled, and thus improves the efficiency, using a decreasing ellipsoidal bound in the n-dimensional parameter space centred on the maximum likelihood point. However, if the likelihood function contains any multi-modality, then the ellipse is prevented from constraining the sampling region efficiently. In this paper we introduce a method of clustered ellipsoidal nested sampling which can form multiple ellipses around each individual peak in the likelihood. In addition we have implemented a method for determining the expectation and variance of the final evidence value without the need to use sampling error from repetitions of the algorithm ; this further reduces the computational load by at least an order of magnitude. We have applied our algorithm to a pair of toy models and one cosmological example where we demonstrate that the number of likelihood evaluations required is ~ 4% of that necessary for using previous algorithms. We have produced a fortran library containing our routines which can be called from any sampling code, in addition for convenience we have incorporated it into the popular CosmoMC code as CosmoClust. Both are available for download at http://www.mrao.cam.ac.uk/software/cosmoclust .Comment: 7 pages, 8 figures, changed to match version accepted by MNRA

Experiences of Interventions Aiming to Improve the Mental Health and Wellbeing of Children and Young People with a Long-Term Physical Condition: A Systematic Review and Meta-ethnography

This is the author accepted manuscript. The final version is available from Wiley via the DOI in this recordBackground Children and young people with long term physical health conditions are at increased risk of experiencing mental health and wellbeing difficulties. However, there is a lack of research that explores the experiences of, and attitudes towards interventions aiming to improve their mental health and wellbeing. This systematic review seeks to address this gap in the literature by exploring what children and young people with long term conditions, their caregivers and health practitioners perceive to be important aspects of interventions aiming to improve their mental health and wellbeing. Methods An information specialist searched five academic databases using pre‐defined criteria for qualitative evaluations of interventions aiming to improve the mental health or wellbeing of children with long term physical conditions. Reviewers also performed supplementary citation and grey literature searches. Two reviewers independently screened titles, abstracts and full texts which met the inclusion criteria and conducted data extraction and quality assessment. Meta‐ethnography was used to synthesise the findings. Results Screening identified 60 relevant articles. We identified five overarching constructs through the synthesis: i) Getting In and Staying In, ii) Therapeutic Foundation, iii) Social Support, iv) A Hopeful Alternative and v) Empowerment. The line of argument which links these constructs together indicates that when interventions can provide an environment that allows young people to share their experiences and build empathetic relationships; it can enable participants to access social support and increase feelings of hope and empowerment. Conclusion These findings may provide a framework to inform the development of mental health interventions for this population, and evaluate existing interventions which already include some of the components or processes identified by this research. Further research is needed to establish which of the constructs identified by the line of argument are most effective in improving the mental wellbeing of young people living with long term conditions.National Institute for Health Research (NIHR

Utility of Hemoglobin A1c for Diagnosing Prediabetes and Diabetes in Obese Children and Adolescents

OBJECTIVE-Hemoglobin A(1c) (A1C) has emerged as a recommended diagnostic tool for identifying diabetes and subjects at risk for the disease. This recommendation is based on data in adults showing the relationship between A1C with future development of diabetes and microvascular complications. However, studies in the pediatric population are lacking. RESEARCH DESIGN AND METHODS-We studied a multiethnic cohort of 1,156 obese children and adolescents without a diagnosis of diabetes (male, 40%/female, 60%). All subjects underwent an oral glucose tolerance test (OGTT) and A1C measurement. These tests were repeated after a follow-up time of similar to 2 years in 218 subjects. RESULTS-At baseline, subjects were stratified according to A1C categories: 77% with normal glucose tolerance (A1C 6.5%). In the at risk for diabetes category, 47% were classified with prediabetes or diabetes, and in the diabetes category, 62% were classified with type 2 diabetes by the OGTT. The area under the curve receiver operating characteristic for A1C was 0.81 (95% Cl 0.70-0.92). The threshold for identifying type 2 diabetes was 5.8%, with 78% specificity and 68% sensitivity. In the subgroup with repeated measures, a multivariate analysis showed that the strongest predictors of 2-h glucose at follow-up were baseline A1C and 2-h glucose, independently of age, ethnicity, sex, fasting glucose, and follow-up time. CONCLUSIONS-The American Diabetes Association suggested that an A1C of 6.5% underestimates the prevalence of prediabetes and diabetes in obese children and adolescents. Given the low sensitivity and specificity, the use of A1C by itself represents a poor diagnostic tool for prediabetes and type 2 diabetes in obese children and adolescents

Adapting preference-based utility measures to capture the impact of cancer treatment-related symptoms

It is important that patient-reported outcome (PRO) measures used to assess cancer therapies adequately capture the benefits and risks experienced by patients, particularly when adverse event profiles differ across therapies. This study explores the case for augmenting preference-based utility measures to capture the impact of cancer treatment-related symptoms. Additional cancer treatment-related items could be specific (e.g., rash) or global. While specific items are easier to describe and understand, their use may miss rarer symptoms and those that are currently unknown but will arise from future medical advancements. The appropriate number of additional items, the independence of those items, and their impact on the psychometric properties of the core instrument require consideration. Alternatively, a global item could encompass all potential treatment-related symptoms, of any treatments for any disease. However, such an item may not be well understood by general public respondents in valuation exercises. Further challenges include the decision about whether to generate de novo value sets for the modified instrument or to map to existing tariffs. The fluctuating and transient nature of treatment-related symptoms may be inconsistent with the methods used in conventional valuation exercises. Fluctuating symptoms could be missed by sub-optimal measure administration timing. The addition of items also poses double-counting risks. In summary, the addition of treatment-related symptom items could increase the sensitivity of existing utility measures to capture known and unknown treatment effects in oncology, while retaining the core domains. However, more research is needed to investigate the challenges, particularly regarding valuation

The ISW-tSZ cross correlation: ISW extraction out of pure CMB data

If Dark Energy introduces an acceleration in the universal expansion then large scale gravitational potential wells should be shrinking, causing a blueshift in the CMB photons that cross such structures (Integrated Sachs-Wolfe effect, [ISW]). Galaxy clusters are known to probe those potential wells. In these objects, CMB photons also experience inverse Compton scattering off the hot electrons of the intra-cluster medium, and this results in a distortion with a characteristic spectral signature of the CMB spectrum (the so-called thermal Sunyaev-Zel'dovich effect, [tSZ]). Since both the ISW and the tSZ effects take place in the same potential wells, they must be spatially correlated. We present how this cross ISW-tSZ signal can be detected in a CMB-data contained way by using the frequency dependence of the tSZ effect in multi frequency CMB experiments like {\it Planck}, {\em without} requiring the use of external large scale structure tracers data. We find that by masking low redshift clusters, the shot noise level decreases significantly, boosting the signal to noise ratio of the ISW--tSZ cross correlation. We also find that galactic and extragalactic dust residuals must be kept at or below the level of ~0.04 muK^2 at l=10, a limit that is a factor of a few below {\it Planck}'s expectations for foreground subtraction. If this is achieved, CMB observations of the ISW-tSZ cross correlation should also provide an independent probe for the existence of Dark Energy and the amplitude of density perturbations.Comment: submitted to MNRA

The Atacama Cosmology Telescope: Cosmological Parameters from the 2008 Power Spectra

We present cosmological parameters derived from the angular power spectrum of the cosmic microwave background (CMB) radiation observed at 148 GHz and 218 GHz over 296 deg^2 with the Atacama Cosmology Telescope (ACT) during its 2008 season. ACT measures fluctuations at scales 500<l<10000. We fit a model for the lensed CMB, Sunyaev-Zel'dovich (SZ), and foreground contribution to the 148 GHz and 218 GHz power spectra, including thermal and kinetic SZ, Poisson power from radio and infrared point sources, and clustered power from infrared point sources. The power from thermal and kinetic SZ at 148 GHz is estimated to be B_3000 = 6.8+-2.9 uK^2, where B_l=l(l+1)C_l/2pi. We estimate primary cosmological parameters from the 148 GHz spectrum, marginalizing over SZ and source power. The LCDM cosmological model is a good fit to the data, and LCDM parameters estimated from ACT+WMAP are consistent with the 7-year WMAP limits, with scale invariant n_s = 1 excluded at 99.7% CL (3sigma). A model with no CMB lensing is disfavored at 2.8sigma. By measuring the third to seventh acoustic peaks, and probing the Silk damping regime, the ACT data improve limits on cosmological parameters that affect the small-scale CMB power. The ACT data combined with WMAP give a 6sigma detection of primordial helium, with Y_P = 0.313+-0.044, and a 4sigma detection of relativistic species, assumed to be neutrinos, with Neff = 5.3+-1.3 (4.6+-0.8 with BAO+H0 data). From the CMB alone the running of the spectral index is constrained to be dn/dlnk = -0.034 +- 0.018, the limit on the tensor-to-scalar ratio is r<0.25 (95% CL), and the possible contribution of Nambu cosmic strings to the power spectrum is constrained to string tension Gmu<1.6 \times 10^-7 (95% CL).Comment: 20 pages, 13 figures. Submitted to ApJ. This paper is a companion to Hajian et al. (2010) and Das et al. (2010

Quantum Convolutional Coding with Shared Entanglement: General Structure

We present a general theory of entanglement-assisted quantum convolutional coding. The codes have a convolutional or memory structure, they assume that the sender and receiver share noiseless entanglement prior to quantum communication, and they are not restricted to possess the Calderbank-Shor-Steane structure as in previous work. We provide two significant advances for quantum convolutional coding theory. We first show how to "expand" a given set of quantum convolutional generators. This expansion step acts as a preprocessor for a polynomial symplectic Gram-Schmidt orthogonalization procedure that simplifies the commutation relations of the expanded generators to be the same as those of entangled Bell states (ebits) and ancilla qubits. The above two steps produce a set of generators with equivalent error-correcting properties to those of the original generators. We then demonstrate how to perform online encoding and decoding for a stream of information qubits, halves of ebits, and ancilla qubits. The upshot of our theory is that the quantum code designer can engineer quantum convolutional codes with desirable error-correcting properties without having to worry about the commutation relations of these generators.Comment: 23 pages, replaced with final published versio