arXiv subjects

F. Feroz

Publications and source records attributed to F. Feroz.

36 records · Page 2Linked to original sources

arXiv2011

Bayesian evidence for two companions orbiting HIP 5158

We present results of a Bayesian analysis of radial velocity (RV) data for the star HIP 5158, confirming the presence of two companions and also constraining their orbital parameters. Assuming Keplerian orbits, the two-companion model is found to be e^{48} times more probable than the one-planet model, although the orbital parameters of the second companion are only weakly constrained. The derived orbital periods are 345.6 +/- 2.0 d and 9017.8 +/- 3180.7 d respectively, and the corresponding eccentricities are 0.54 +/- 0.04 and 0.14 +/- 0.10. The limits on planetary mass (m \sin i) and semimajor axis are (1.44 +/- 0.14 M_{J}, 0.89 +/- 0.01 AU) and (15.04 +/- 10.55 M_{J}, 7.70 +/- 1.88 AU) respectively. Owing to large uncertainty on the mass of the second companion, we are unable to determine whether it is a planet or a brown dwarf. The remaining `noise' (stellar jitter) unaccounted for by the model is 2.28 +/- 0.31 m/s. We also analysed a three-companion model, but found it to be e^{8} times less probable than the two-companion model.

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arXiv2011

Planck Early Results VIII: The all-sky Early Sunyaev-Zeldovich cluster sample

We present the first all-sky sample of galaxy clusters detected blindly by the Planck satellite through the Sunyaev-Zeldovich (SZ) effect from its six highest frequencies. This early SZ (ESZ) sample is comprised of 189 candidates, which have a high signal-to-noise ratio ranging from 6 to 29. Its high reliability (purity above 95%) is further ensured by an extensive validation process based on Planck internal quality assessments and by external cross-identification and follow-up observations. Planck provides the first measured SZ signal for about 80% of the 169 previously-known ESZ clusters. Planck furthermore releases 30 new cluster candidates, amongst which 20 meet the ESZ signal-to-noise selection criterion. At the submission date, twelve of the 20 ESZ candidates were confirmed as new clusters, with eleven confirmed using XMM-Newton snapshot observations, most of them with disturbed morphologies and low luminosities. The ESZ clusters are mostly at moderate redshifts (86% with z below 0.3) and span more than a decade in mass, up to the rarest and most massive clusters with masses above 10^15 Msol.

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arXiv2011

Challenges of Profile Likelihood Evaluation in Multi-Dimensional SUSY Scans

Statistical inference of the fundamental parameters of supersymmetric theories is a challenging and active endeavor. Several sophisticated algorithms have been employed to this end. While Markov-Chain Monte Carlo (MCMC) and nested sampling techniques are geared towards Bayesian inference, they have also been used to estimate frequentist confidence intervals based on the profile likelihood ratio. We investigate the performance and appropriate configuration of MultiNest, a nested sampling based algorithm, when used for profile likelihood-based analyses both on toy models and on the parameter space of the Constrained MSSM. We find that while the standard configuration is appropriate for an accurate reconstruction of the Bayesian posterior, the profile likelihood is poorly approximated. We identify a more appropriate MultiNest configuration for profile likelihood analyses, which gives an excellent exploration of the profile likelihood (albeit at a larger computational cost), including the identification of the global maximum likelihood value. We conclude that with the appropriate configuration MultiNest is a suitable tool for profile likelihood studies, indicating previous claims to the contrary are not well founded.

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arXiv2011

Detecting extrasolar planets from stellar radial velocities using Bayesian evidence

Stellar radial velocity (RV) measurements have proven to be a very successful method for detecting extrasolar planets. Analysing RV data to determine the parameters of the extrasolar planets is a significant statistical challenge owing to the presence of multiple planets and various degeneracies between orbital parameters. Determining the number of planets favoured by the observed data is an even more difficult task. Bayesian model selection provides a mathematically rigorous solution to this problem by calculating marginal posterior probabilities of models with different number of planets, but the use of this method in extrasolar planetary searches has been hampered by the computational cost of the evaluating Bayesian evidence. Nonetheless, Bayesian model selection has the potential to improve the interpretation of existing observational data and possibly detect yet undiscovered planets. We present a new and efficient Bayesian method for determining the number of extrasolar planets, as well as for inferring their orbital parameters, without having to calculate directly the Bayesian evidence for models containing a large number of planets. Instead, we work iteratively and at each iteration obtain a conservative lower limit on the odds ratio for the inclusion of an additional planet into the model. We apply this method to simulated data-sets containing one and two planets and successfully recover the correct number of planets and reliable constraints on the orbital parameters. We also apply our method to RV measurements of HD 37124, 47 Ursae Majoris and HD 10180. For HD 37124, we confirm that the current data strongly favour a three-planet system. We find strong evidence for the presence of a fourth planet in 47 Ursae Majoris, but its orbital period is suspiciously close to one year, casting doubt on its validity. For HD 10180 we find strong evidence for a six-planet system.

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arXiv2011

A Coverage Study of the CMSSM Based on ATLAS Sensitivity Using Fast Neural Networks Techniques

We assess the coverage properties of confidence and credible intervals on the CMSSM parameter space inferred from a Bayesian posterior and the profile likelihood based on an ATLAS sensitivity study. In order to make those calculations feasible, we introduce a new method based on neural networks to approximate the mapping between CMSSM parameters and weak-scale particle masses. Our method reduces the computational effort needed to sample the CMSSM parameter space by a factor of ~ 10^4 with respect to conventional techniques. We find that both the Bayesian posterior and the profile likelihood intervals can significantly over-cover and identify the origin of this effect to physical boundaries in the parameter space. Finally, we point out that the effects intrinsic to the statistical procedure are conflated with simplifications to the likelihood functions from the experiments themselves.

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arXiv2010

Selecting a Model of Supersymmetry Breaking Mediation

We study the problem of selecting between different mechanisms of supersymmetry breaking in the Minimal Supersymmetric Standard Model using current data. We evaluate the Bayesian evidence of four supersymmetry breaking scenarios: mSUGRA, mGMSB, mAMSB and moduli mediation. The results show a strong dependence on the dark matter assumption. Using the inferred cosmological relic density as an upper bound, minimal anomaly mediation is at least moderately favoured over the CMSSM. Our fits also indicate that evidence for a positive sign of the mu parameter is moderate at best. We present constraints on the anomaly and gauge mediated parameter spaces and some previously unexplored aspects of the dark matter phenomenology of the moduli mediation scenario. We use sparticle searches, indirect observables and dark matter observables in the global fit and quantify robustness with respect to prior choice. We quantify how much information is contained within each constraint.

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arXiv2010

MSSM dark matter measurements at the LHC without squarks and sleptons

We examine the case of neutralino dark matter in the focus point region of the MSSM, in which the scalar sparticles are too heavy to be produced at the LHC. Whilst it has been previously asserted that the LHC alone would fail to constrain the properties of the lightest neutralino for such a scenario, we find that one can obtain good predictions of astrophysical quantities such as the relic density, annihilation cross-section and direct search cross-sections by using the shape of the dilepton invariant mass spectrum to constrain neutralino mixing. We demonstrate our technique using a Bayesian analysis of the 24 parameter MSSM model space, and in the process introduce a novel way of improving the LHC results even without assumptions on which new sparticles are responsible for the kinematic features in the dilepton invariant mass distribution.

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arXiv2010

Fitting the Phenomenological MSSM

We perform a global Bayesian fit of the phenomenological minimal supersymmetric standard model (pMSSM) to current indirect collider and dark matter data. The pMSSM contains the most relevant 25 weak-scale MSSM parameters, which are simultaneously fit using `nested sampling' Monte Carlo techniques in more than 15 years of CPU time. We calculate the Bayesian evidence for the pMSSM and constrain its parameters and observables in the context of two widely different, but reasonable, priors to determine which inferences are robust. We make inferences about sparticle masses, the sign of the $μ$ parameter, the amount of fine tuning, dark matter properties and the prospects for direct dark matter detection without assuming a restrictive high-scale supersymmetry breaking model. We find the inferred lightest CP-even Higgs boson mass as an example of an approximately prior independent observable. This analysis constitutes the first statistically convergent pMSSM global fit to all current data.

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arXiv2010

Comment on "Bayesian evidence: can we beat MultiNest using traditional MCMC methods", by Rutger van Haasteren (arXiv:0911.2150)

In arXiv:0911.2150, Rutger van Haasteren seeks to criticize the nested sampling algorithm for Bayesian data analysis in general and its MultiNest implementation in particular. He introduces a new method for evidence evaluation based on the idea of Voronoi tessellation and requiring samples from the posterior distribution obtained through MCMC based methods. He compares its accuracy and efficiency with MultiNest, concluding that it outperforms MultiNest in several cases. This comparison is completely unfair since the proposed method can not perform the complete Bayesian data analysis including posterior exploration and evidence evaluation on its own while MultiNest allows one to perform Bayesian data analysis end to end. Furthermore, their criticism of nested sampling (and in turn MultiNest) is based on a few conceptual misunderstandings of the algorithm. Here we seek to set the record straight.

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arXiv2009

Are BR(b->s gamma) and (g-2)_muon consistent within the Constrained MSSM?

We employ two different statistical tests to examine whether, in the framework of the Constrained MSSM, the experimentally determined values of BR(b->s gamma) and the anomalous magnetic moment of the muon, (g-2), are consistent with each other. Our tests are designed to compare the theoretical predictions of the CMSSM in data space with the actual measurements, once all of the CMSSM free parameters have been integrated out and constrained using all other available data. We investigate the value of (g-2) as obtained by using e+e- data alone (which shows a ~3sigma discrepancy with the SM prediction) and as obtained based on tau decay data (which shows a much milder, 1sigma discrepancy). We find that one of our tests returns either a statistically inconclusive result or shows weak evidence of tension between BR(b->s gamma) and the e+e- data based value of (g-2). On the other hand, our second test, which is more stringent in this application, reveals that the joint observations of BR(b->s gamma) and (g-2) from e+e- data alone are incompatible within the CMSSM at the ~2sigma level. On the other hand, for both tests we find no significant tension between BR(b->s gamma) and the value of (g-2) evaluated using tau decay data. These results are only weakly dependent on the three different priors that we employ in the analysis. We conclude that, if the discrepancy between the Standard Model and the experimental determinations of (g-2) is confirmed at the 3sigma level, this could be interpreted as strong evidence against the CMSSM.

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arXiv2008

Bayesian optimal reconstruction of the primordial power spectrum

The form of the primordial power spectrum has the potential to differentiate strongly between competing models of perturbation generation in the early universe and so is of considerable importance. The recent release of five years of WMAP observations have confirmed the general picture of the primordial power spectrum as deviating slightly from scale invariance with a spectral tilt parameter of n_s ~ 0.96. Nonetheless, many attempts have been made to isolate further features such as breaks and cutoffs using a variety of methods, some employing more than ~ 10 varying parameters. In this paper we apply the robust technique of Bayesian model selection to reconstruct the optimal degree of structure in the spectrum. We model the spectrum simply and generically as piecewise linear in ln k between `nodes' in k-space whose amplitudes are allowed to vary. The number of nodes and their k-space positions are chosen by the Bayesian evidence so that we can identify both the complexity and location of any detected features. Our optimal reconstruction contains, perhaps, surprisingly few features, the data preferring just three nodes. This reconstruction allows for a degree of scale dependence of the tilt with the `turn-over' scale occuring around k ~ 0.016 Mpc^{-1}. More structure is penalised by the evidence as over-fitting the data, so there is currently little point in attempting reconstructions that are more complex.

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arXiv2008

The impact of priors and observables on parameter inferences in the Constrained MSSM

We use a newly released version of the SuperBayeS code to analyze the impact of the choice of priors and the influence of various constraints on the statistical conclusions for the preferred values of the parameters of the Constrained MSSM. We assess the effect in a Bayesian framework and compare it with an alternative likelihood-based measure of a profile likelihood. We employ a new scanning algorithm (MultiNest) which increases the computational efficiency by a factor ~200 with respect to previously used techniques. We demonstrate that the currently available data are not yet sufficiently constraining to allow one to determine the preferred values of CMSSM parameters in a way that is completely independent of the choice of priors and statistical measures. While b->s gamma generally favors large m_0, this is in some contrast with the preference for low values of m_0 and m_1/2 that is almost entirely a consequence of a combination of prior effects and a single constraint coming from the anomalous magnetic moment of the muon, which remains somewhat controversial. Using an information-theoretical measure, we find that the cosmological dark matter abundance determination provides at least 80% of the total constraining power of all available observables. Despite the remaining uncertainties, prospects for direct detection in the CMSSM remain excellent, with the spin-independent neutralino-proton cross section almost guaranteed above sigma_SI ~ 10^{-10} pb, independently of the choice of priors or statistics. Likewise, gluino and lightest Higgs discovery at the LHC remain highly encouraging. While in this work we have used the CMSSM as particle physics model, our formalism and scanning technique can be readily applied to a wider class of models with several free parameters.

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arXiv2008

Bayesian modelling of clusters of galaxies from multi-frequency pointed Sunyaev--Zel'dovich observations

We present a Bayesian approach to modelling galaxy clusters using multi-frequency pointed observations from telescopes that exploit the Sunyaev--Zel'dovich effect. We use the recently developed MultiNest technique (Feroz, Hobson & Bridges, 2008) to explore the high-dimensional parameter spaces and also to calculate the Bayesian evidence. This permits robust parameter estimation as well as model comparison. Tests on simulated Arcminute Microkelvin Imager observations of a cluster, in the presence of primary CMB signal, radio point sources (detected as well as an unresolved background) and receiver noise, show that our algorithm is able to analyse jointly the data from six frequency channels, sample the posterior space of the model and calculate the Bayesian evidence very efficiently on a single processor. We also illustrate the robustness of our detection process by applying it to a field with radio sources and primordial CMB but no cluster, and show that indeed no cluster is identified. The extension of our methodology to the detection and modelling of multiple clusters in multi-frequency SZ survey data will be described in a future work.

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arXiv2008

Bayesian Selection of sign(mu) within mSUGRA in Global Fits Including WMAP5 Results

We study the properties of the constrained minimal supersymmetric standard model (mSUGRA) by performing fits to updated indirect data, including the relic density of dark matter inferred from WMAP5. In order to find the extent to which mu < 0 is disfavoured compared to mu > 0, we compare the Bayesian evidence values for these models, which we obtain straightforwardly and with good precision from the recently developed multi-modal nested sampling ('MultiNest') technique. We find weak to moderate evidence for the mu > 0 branch of mSUGRA over mu < 0 and estimate the ratio of probabilities to be P(mu > 0)/P(mu < 0) = 6-61 depending on the prior measure and range used. There is thus positive (but not overwhelming) evidence that mu > 0 in mSUGRA. The MultiNest technique also delivers probability distributions of parameters and other relevant quantities such as superpartner masses. We explore the dependence of our results on the choice of the prior measure used. We also use the Bayesian evidence to quantify the consistency between the mSUGRA parameter inferences coming from the constraints that have the largest effects: (g-2)_mu, BR(b -> s gamma) and cold dark matter (DM) relic density Omega_{DM}h^2.

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arXiv2008

Cluster detection in weak lensing surveys

We present an efficient and robust approach for extracting clusters of galaxies from weak lensing survey data and measuring their properties. We use simple, physically-motivated cluster models appropriate for such sparse, noisy data, and incorporate our knowledge of the cluster mass function to optimise the detection of low-mass objects. Despite the method's non-linear nature, we are able to search at a rate of approximately half a square degree per hour on a single processor, making this technique a viable candidate for future wide-field surveys. We quantify, for two simulated data-sets, the accuracy of recovered cluster parameters, and discuss the completeness and purity of our shear-selected cluster catalogues.

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arXiv2008

MultiNest: an efficient and robust Bayesian inference tool for cosmology and particle physics

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 (2008), which itself significantly outperformed existing MCMC techniques in a wide range of astrophysical inference problems. The accuracy and economy of the MultiNest algorithm is demonstrated by application to two toy problems and to a cosmological inference problem focussing on the extension of the vanilla $Λ$CDM 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

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arXiv2008

The Arcminute Microkelvin Imager

The Arcminute Microkelvin Imager is a pair of interferometer arrays operating with six frequency channels spanning 13.9-18.2 GHz, with very high sensitivity to angular scales 30''-10'. The telescope is aimed principally at Sunyaev-Zel'dovich imaging of clusters of galaxies. We discuss the design of the telescope and describe and explain its electronic and mechanical systems.

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arXiv2007

AMI limits on 15 GHz excess emission in northern HII regions

We present observations between 14.2 and 17.9 GHz of sixteen Galactic HII regions made with the Arcminute Microkelvin Imager (AMI). In conjunction with data from the literature at lower radio frequencies we investigate the possibility of a spinning dust component in the spectra of these objects. We conclude that there is no significant evidence for spinning dust towards these sources and measure an average spectral index of 0.15+/-0.07 between 1.4 and 17.9 GHz for the sample.

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