arXiv subjects

M. Bridges

Publications and source records attributed to M. Bridges.

50 records · Page 3Linked to original sources

arXiv2012

Constraints on fNL from Wilkinson Microwave Anisotropy Probe 7-year data using a neural network classifier

We present a multi-class neural network (NN) classifier as a method to measure nonGaussianity, characterised by the local non-linear coupling parameter fNL, in maps of the cosmic microwave background (CMB) radiation. The classifier is trained on simulated non-Gaussian CMB maps with a range of known fNL values by providing it with wavelet coefficients of the maps; we consider both the HealPix (HW) wavelet and the spherical Mexican hat wavelet (SMHW). When applied to simulated test maps, the NN classfier produces results in very good agreement with those obtained using standard chi2 minimization. The standard deviations of the fNL estimates for WMAPlike simulations were σ = 22 and σ = 33 for the SMHW and the HW, respectively, which are extremely close to those obtained using classical statistical methods in Curto et al. and Casaponsa et al. Moreover, the NN classifier does not require the inversion of a large covariance matrix, thus avoiding any need to regularise the matrix when it is not directly invertible, and is considerably faster.

astro-ph.CO↗

arXiv2012

A Bayesian study of the primordial power spectrum from a novel closed universe model

We constrain the shape of the primordial power spectrum using recent measurements of the cosmic microwave background (CMB) from the Wilkinson Microwave Anisotropy Probe (WMAP) 7-year data and other high-resolution CMB experiments. We also include observations of the matter power spectrum from the luminous red galaxy (LRG) subset DR7 of the Sloan Digital Sky Survey (SDSS). We consider two different models of the primordial power spectrum. The first is the standard nearly scale-invariant spectrum in the form of a generalised power-law parameterised in terms of the spectral amplitude $A_{\rm s}$, the spectral index $n_{\rm s}$ and (possibly) the running parameter $n_{\rm run}$. The second spectrum is derived from the Lasenby and Doran (LD) model. The LD model is based on the restriction of the total conformal time available in a closed Universe and the predicted primordial power spectrum depends upon just two parameters. An important feature of the LD spectrum is that it naturally incorporates an exponential fall-off on large scales, which might provide a possible explanation for the lower-than-expected power observed at low multipoles in the CMB. In addition to parameter estimation, we compare both models using Bayesian model selection. We find there is a significant preference for the LD model over a simple power-law spectrum for a CMB-only dataset, and over models with an equal number of parameters for all the datasets considered.

astro-ph.CO↗

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.

hep-ph↗

arXiv2010

Genetic Classification of Populations using Supervised Learning

There are many instances in genetics in which we wish to determine whether two candidate populations are distinguishable on the basis of their genetic structure. Examples include populations which are geographically separated, case--control studies and quality control (when participants in a study have been genotyped at different laboratories). This latter application is of particular importance in the era of large scale genome wide association studies, when collections of individuals genotyped at different locations are being merged to provide increased power. The traditional method for detecting structure within a population is some form of exploratory technique such as principal components analysis. Such methods, which do not utilise our prior knowledge of the membership of the candidate populations. are termed \emph{unsupervised}. Supervised methods, on the other hand are able to utilise this prior knowledge when it is available. In this paper we demonstrate that in such cases modern supervised approaches are a more appropriate tool for detecting genetic differences between populations. We apply two such methods, (neural networks and support vector machines) to the classification of three populations (two from Scotland and one from Bulgaria). The sensitivity exhibited by both these methods is considerably higher than that attained by principal components analysis and in fact comfortably exceeds a recently conjectured theoretical limit on the sensitivity of unsupervised methods. In particular, our methods can distinguish between the two Scottish populations, where principal components analysis cannot. We suggest, on the basis of our results that a supervised learning approach should be the method of choice when classifying individuals into pre-defined populations, particularly in quality control for large scale genome wide association studies.

q-bio.QM↗

arXiv2009

The Origin of the Universe as Revealed Through the Polarization of the Cosmic Microwave Background

Modern cosmology has sharpened questions posed for millennia about the origin of our cosmic habitat. The age-old questions have been transformed into two pressing issues primed for attack in the coming decade: How did the Universe begin? and What physical laws govern the Universe at the highest energies? The clearest window onto these questions is the pattern of polarization in the Cosmic Microwave Background (CMB), which is uniquely sensitive to primordial gravity waves. A detection of the special pattern produced by gravity waves would be not only an unprecedented discovery, but also a direct probe of physics at the earliest observable instants of our Universe. Experiments which map CMB polarization over the coming decade will lead us on our first steps towards answering these age-old questions.

astro-ph.CO↗

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.

astro-ph↗

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

astro-ph↗

arXiv2007

Bianchi VII_h models and the cold spot texture

We have returned to our previous Bianchi VII_h analysis in light of the Cruz et al. 2007 suggestion that the cold spot observed near the southern Galactic pole may be a remnant temperature perturbation of a cosmic texture. In Bridges et al. 2006b we found two favoured left handed Bianchi VII_h templates with restricted prior probabilities so that the template was centred close to the cold spot. Using WMAP data `corrected' for the texture fit we have now reexamined both models to assess any changes to these conclusions. We find that both models are left almost entirely unconstrained by the data and consequently exhibit significantly reduced Bayesian evidences. Both models are now disfavoured by the data. This result reinforces our previous suggestion that the cold spot was likely to be driving any Bianchi VII_h detection.

astro-ph↗

arXiv2007

Markov chain Monte Carlo analysis of Bianchi VII_h models

We have extended the analysis of Jaffe et al. to a complete Markov chain Monte Carlo (MCMC) study of the Bianchi type ${\rm VII_h}$ models including a dark energy density, using 1-year and 3-year Wilkinson Microwave Anisotropy Probe (WMAP) cosmic microwave background (CMB) data. Since we perform the analysis in a Bayesian framework our entire inference is contained in the multidimensional posterior distribution from which we can extract marginalised parameter constraints and the comparative Bayesian evidence. Treating the left-handed Bianchi CMB anisotropy as a template centred upon the `cold-spot' in the southern hemisphere, the parameter estimates derived for the total energy density, `tightness' and vorticity from 3-year data are found to be: $Ω_{tot} = 0.43\pm 0.04$, $h = 0.32^{+0.02}_{-0.13}$, $ω= 9.7^{+1.6}_{-1.5}\times 10^{-10}$ with orientation $γ= {337^{\circ}}^{+17}_{-23}$). This template is preferred by a factor of roughly unity in log-evidence over a concordance cosmology alone. A Bianchi type template is supported by the data only if its position on the sky is heavily restricted. The low total energy density of the preferred template, implies a geometry that is incompatible with cosmologies inferred from recent CMB observations. Jaffe et al. found that extending the Bianchi model to include a term in $Ω_Λ$ creates a degeneracy in the $Ω_m - Ω_Λ$ plane. We explore this region fully by MCMC and find that the degenerate likelihood contours do not intersect areas of parameter space that 1 or 3 year WMAP data would prefer at any significance above $2σ$. Thus we can confirm that a physical Bianchi ${\rm VII_h}$ model is not responsible for this signature.

astro-ph↗

arXiv2007

Fast cosmological parameter estimation using neural networks

We present a method for accelerating the calculation of CMB power spectra, matter power spectra and likelihood functions for use in cosmological parameter estimation. The algorithm, called CosmoNet, is based on training a multilayer perceptron neural network and shares all the advantages of the recently released Pico algorithm of Fendt & Wandelt, but has several additional benefits in terms of simplicity, computational speed, memory requirements and ease of training. We demonstrate the capabilities of CosmoNet by computing CMB power spectra over a box in the parameter space of flat ΛCDM models containing the 3σWMAP1 confidence region. We also use CosmoNet to compute the WMAP3 likelihood for flat ΛCDM models and show that marginalised posteriors on parameters derived are very similar to those obtained using CAMB and the WMAP3 code. We find that the average error in the power spectra is typically 2-3% of cosmic variance, and that CosmoNet is \sim 7 \times 10^4 faster than CAMB (for flat models) and \sim 6 \times 10^6 times faster than the official WMAP3 likelihood code. CosmoNet and an interface to CosmoMC are publically available at www.mrao.cam.ac.uk/software/cosmonet.

astro-ph↗

arXiv2007

A Bayesian analysis of the primordial power spectrum

We present a Bayesian analysis of large-scale structure and cosmic microwave background data to constrain the form of the primordial power spectrum. We have extended the usual presumption of a scale invariant spectrum to include: (i) a running spectral index; (ii) a broken spectrum arising perhaps from an interruption of the potential driving inflation; (iii) a large scale cutoff in power as the first year WMAP results appear to indicate; (iv) a reconstruction of the spectrum in eight bins in wavenumber; and (v) a spectrum resulting from a cosmological model proposed by Lasenby & Doran, which naturally exhibits an exponential drop in power on very large scales. The result of our complete Bayesian analysis includes not only the posterior probability distribution from which parameter estimates are inferred but also the Bayesian evidence. This evidence value is greater for a model with fewer parameters unless a more complicated model provides a significantly better fit to the data, thus allowing a powerful method of model selection. We find that those models exhibiting any form of cutoff in power on large scales consistently produce higher evidences than either the Harrison-Zel'dovich or single spectral index spectra. In particular, within the best-fit concordance cosmology, we find the Lasenby & Doran spectrum to show significantly larger evidence as compared to the other models.

astro-ph↗

arXiv2007

WMAP 3-year primordial power spectrum

We constrain the form of the primordial power spectrum using Wilkinson Microwave Anisotropy Probe (WMAP) 3-year cosmic microwave background (CMB) data (+ other high resolution CMB experiments) in addition to complementary large-scale structure (LSS) data: 2dF, SDSS, Ly-alpha forest and luminous red galaxy (LRG) data from the SDSS catalogue. We compute the comparative Bayesian evidence in addition to parameter estimates for a collection of seven models: (i) a scale invariant Harrison-Zel'dovich (H-Z) spectrum; (ii) a power-law; (iii) a running spectral index; (iv) a broken spectrum; (v) a power-law with an abrupt cutoff on large-scales; (vi) a reconstruction of the spectrum in eight bins in wavenumber; and (vii) a spectrum resulting from a cosmological model proposed by Lasenby & Doran (L-D). Using a basic dataset of WMAP3 + other CMB + 2dF + SDSS our analysis confirms that a scale-invariant spectrum is disfavoured by between 0.7 and 1.7 units of log evidence (depending on priors chosen) when compared with a power-law tilt. Moreover a running spectrum is now significantly preferred, but only when using the most constraining set of priors. The addition of Ly-alpha and LRG data independently both suggest much lower values of the running index than with basic dataset alone and interestingly the inclusion of Ly-alpha significantly disfavours a running parameterisation by more than a unit in log evidence. Overall the highest evidences, over all datasets, were obtained with a power law spectrum containing a cutoff with a significant log evidence difference of roughly 2 units. The natural tilt and exponential cutoff present in the L-D spectrum is found to be favoured decisively by a log evidence difference of over 5 units, but only for a limited study within the best-fit concordance cosmology.

astro-ph↗

arXiv2007

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 .

astro-ph↗

arXiv2007

{\sc CosmoNet}: fast cosmological parameter estimation in non-flat models using neural networks

We present a further development of a method for accelerating the calculation of CMB power spectra, matter power spectra and likelihood functions for use in cosmological Bayesian inference. The algorithm, called {\sc CosmoNet}, is based on training a multilayer perceptron neural network. We compute CMB power spectra (up to $\ell=2000$) and matter transfer functions over a hypercube in parameter space encompassing the $4σ$ confidence region of a selection of CMB (WMAP + high resolution experiments) and large scale structure surveys (2dF and SDSS). We work in the framework of a generic 7 parameter non-flat cosmology. Additionally we use {\sc CosmoNet} to compute the WMAP 3-year, 2dF and SDSS likelihoods over the same region. We find that the average error in the power spectra is typically well below cosmic variance for spectra, and experimental likelihoods calculated to within a fraction of a log unit. We demonstrate that marginalised posteriors generated with {\sc CosmoNet} spectra agree to within a few percent of those generated by {\sc CAMB} parallelised over 4 CPUs, but are obtained 2-3 times faster on just a \emph{single} processor. Furthermore posteriors generated directly via {\sc CosmoNet} likelihoods can be obtained in less than 30 minutes on a single processor, corresponding to a speed up of a factor of $\sim 32$. We also demonstrate the capabilities of {\sc CosmoNet} by extending the CMB power spectra and matter transfer function training to a more generic 10 parameter cosmological model, including tensor modes, a varying equation of state of dark energy and massive neutrinos. {\sc CosmoNet} and interfaces to both {\sc CosmoMC} and {\sc Bayesys} are publically available at {\tt www.mrao.cam.ac.uk/software/cosmonet}.

astro-ph↗