We present further development and the first public release of our multimodal nested sampling algorithm, called MultiNest. This Bayesian inference tool calculates the evidence, with an associated ...error estimate, and produces posterior samples from distributions that may contain multiple modes and pronounced (curving) degeneracies in high dimensions. The developments presented here lead to further substantial improvements in sampling efficiency and robustness, as compared to the original algorithm presented in Feroz & Hobson, which itself significantly outperformed existing Markov chain Monte Carlo techniques in a wide range of astrophysical inference problems. The accuracy and economy of the MultiNest algorithm are demonstrated by application to two toy problems and to a cosmological inference problem focusing on the extension of the vanilla Λ cold dark matter model to include spatial curvature and a varying equation of state for dark energy. The MultiNest software, which is fully parallelized using MPI and includes an interface to CosmoMC, is available at http://www.mrao.cam.ac.uk/software/multinest/. It will also be released as part of the SuperBayeS package, for the analysis of supersymmetric theories of particle physics, at http://www.superbayes.org.
polychord: nested sampling for cosmology Handley, W. J; Hobson, M. P; Lasenby, A. N
Monthly notices of the Royal Astronomical Society. Letters,
06/2015, Letnik:
450, Številka:
1
Journal Article
Recenzirano
Odprti dostop
polychord is a novel nested sampling algorithm tailored for high-dimensional parameter spaces. In addition, it can fully exploit a hierarchy of parameter speeds such as is found in cosmomc and camb. ...It utilizes slice sampling at each iteration to sample within the hard likelihood constraint of nested sampling. It can identify and evolve separate modes of a posterior semi-independently and is parallelized using openmpi. polychord is available for download at http://ccpforge.cse.rl.ac.uk/gf/project/polychord/.
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 Markov Chain Monte Carlo (MCMC) sampling methods. Secondly, in selecting between a set of competing models, calculation of the Bayesian evidence for each model is computationally expensive using existing methods such as thermodynamic integration. The nested sampling method introduced by Skilling, has greatly reduced the computational expense of calculating evidence and also produces posterior inferences as a by-product. This method has been applied successfully in cosmological applications by Mukherjee, Parkinson & Liddle, but their implementation was efficient only for unimodal distributions without pronounced degeneracies. Shaw, Bridges & Hobson 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 in very high dimensions; 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 two 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 data sets, and show that they significantly outperform existing MCMC techniques. An implementation of our methods will be publicly released shortly.
polychord: next-generation nested sampling Handley, W. J; Hobson, M. P; Lasenby, A. N
Monthly notices of the Royal Astronomical Society,
11/2015, Letnik:
453, Številka:
4
Journal Article
Recenzirano
Odprti dostop
polychord is a novel nested sampling algorithm tailored for high-dimensional parameter spaces. This paper coincides with the release of polychord v1.6, and provides an extensive account of the ...algorithm. polychord utilizes slice sampling at each iteration to sample within the hard likelihood constraint of nested sampling. It can identify and evolve separate modes of a posterior semi-independently, and is parallelized using openmpi. It is capable of exploiting a hierarchy of parameter speeds such as those present in cosmomc and camb, and is now in use in the cosmochord and modechord codes. polychord is available for download from http://ccpforge.cse.rl.ac.uk/gf/project/polychord/.
A new Bayesian software package for the analysis of pulsar timing data is presented in the form of temponest which allows for the robust determination of the non-linear pulsar timing solution ...simultaneously with a range of additional stochastic parameters. This includes both red spin noise and dispersion measure variations using either power-law descriptions of the noise, or through a model-independent method that parametrizes the power at individual frequencies in the signal. We use temponest to show that at noise levels representative of current data sets in the European Pulsar Timing Array and International Pulsar Timing Array the linear timing model can underestimate the uncertainties of the timing solution by up to an order of magnitude. We also show how to perform Bayesian model selection between different sets of timing model and stochastic parameters, for example, by demonstrating that in the pulsar B1937+21 both the dispersion measure variations and spin noise in the data are optimally modelled by simple power laws. Finally, we show that not including the stochastic parameters simultaneously with the timing model can lead to unpredictable variation in the estimated uncertainties, compromising the robustness of the scientific results extracted from such analysis.
We consider Weyl gauge theories of gravity (WGTs), which are invariant both under local Poincaré transformations and local changes of scale. Such theories may be interpreted as gauge theories in ...Minkowski spacetime, but their gravitational interactions are most often reinterpreted geometrically in terms of a Weyl-Cartan spacetime, in which any matter fields then reside. Such a spacetime is a straightforward generalization of Weyl spacetime to include torsion. As first suggested by Einstein, Weyl spacetime is believed to exhibit a so-called second clock effect, which prevents the existence of experimentally observed sharp spectral lines, since the rates of (atomic) clocks depend on their past history. The prevailing view in the literature is that this rules out WGTs as unphysical. Contrary to this viewpoint, we show that if one adopts the natural covariant derivative identified in the geometric interpretation of WGTs, properly takes into account the scaling dimension of physical quantities, and recognizes that Einstein's original objection requires the presence of massive matter fields to represent atoms, observers and clocks, then WGTs do not predict a second clock effect.
Gaps in our understanding of genetic susceptibility to malignant hyperthermia (MH) limit the application and interpretation of genetic diagnosis of the condition. Our aim was to define the prevalence ...and role of variants in the three genes implicated in MH susceptibility in the largest comprehensively phenotyped MH cohort worldwide.
We initially included one individual from each positive family tested in the UK MH Unit since 1971 to detect variants in RYR1, CACNA1S, or STAC3. Screening for genetic variants has been ongoing since 1991 and has involved a range of techniques, most recently next generation sequencing. We assessed the pathogenicity of variants using standard guidelines, including family segregation studies. The prevalence of recurrent variants of unknown significance was compared with the prevalence reported in a large database of sequence variants in low-risk populations.
We have confirmed MH susceptibility in 795 independent families, for 722 of which we have a DNA sample. Potentially pathogenic variants were found in 555 families, with 25 RYR1 and one CACNA1S variants previously unclassified recurrent variants significantly over-represented (P<1×10−7) in our cohort compared with the Exome Aggregation Consortium database. There was genotype–phenotype discordance in 86 of 328 families suitable for segregation analysis. We estimate non-RYR1/CACNA1S/STAC3 susceptibility occurs in 14–23% of MH families.
Our data provide current estimates of the role of variants in RYR1, CACNA1S, and STAC3 in susceptibility to MH in a predominantly white European population.
GJ667C is the least massive component of a triple star system which lies at a distance of about 6.8 pc (22.1 light-year) from the Earth. GJ667C has received much attention recently due to the claims ...that it hosts up to seven planets including three super-Earths inside the habitable zone. We present a Bayesian technique for the analysis of radial velocity (RV) data sets in the presence of correlated noise component ('red noise'), with unknown parameters. We also introduce hyper-parameters in our model in order to deal statistically with under- or overestimated error bars on measured RVs as well as inconsistencies between different data sets. By applying this method to the RV data set of GJ667C, we show that this data set contains a significant correlated (red) noise component with correlation time-scale for HARPS data of the order of 9 d. Our analysis shows that the data only provide strong evidence for the presence of two planets: GJ667Cb and c with periods 7.19 and 28.13 d, respectively, with some hints towards the presence of a third signal with period 91 d. The planetary nature of this third signal is not clear and additional RV observations are required for its confirmation. Previous claims of the detection of additional planets in this system are due the erroneous assumption of white noise. Using the standard white noise assumption, our method leads to the detection of up to five signals in this system. We also find that with the red noise model, the measurement uncertainties from HARPS for this system are underestimated at the level of ∼50 per cent.
We reconsider the widely held view that the Mannheim–Kazanas (MK) vacuum solution for a static, spherically symmetric system in conformal gravity (CG) predicts flat rotation curves, such as those ...observed in galaxies, without the need for dark matter. This prediction assumes that test particles have fixed rest mass and follow timelike geodesics in the MK metric in the vacuum region exterior to a spherically symmetric representation of the galactic mass distribution. Such geodesics are not conformally invariant, however, which leads to an apparent discrepancy with the analogous calculation performed in the conformally equivalent Schwarzschild–de-Sitter (SdS) metric, where the latter does not predict flat rotation curves. This difference arises since the mass of particles in CG must instead be generated dynamically through interaction with a scalar field. The energy-momentum of this required scalar field means that, in a general conformal frame from the equivalence class of CG solutions outside a static, spherically symmetric matter distribution, the spacetime is not given by the MK vacuum solution. A unique frame does exist, however, for which the metric retains the MK form, since the scalar field energy-momentum vanishes despite the field being nonzero and radially dependent. Nonetheless, we show that in both this MK frame and the Einstein frame, in which the scalar field is constant, massive particles follow timelike geodesics of the SdS metric, thereby resolving the apparent frame dependence of physical predictions and unambiguously yielding rotation curves with no flat region. Moreover, we show that attempts to model rising rotation curves by fitting the coefficient of the quadratic term in the SdS metric individually for each galaxy are also precluded, since the scalar field equation of motion introduces an additional constraint relative to the vacuum case, such that the coefficient of the quadratic term in the SdS metric is most naturally interpreted as proportional to a global cosmological constant. We also comment briefly on how our analysis resolves the long-standing uncertainty regarding gravitational lensing in the MK metric.
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