M. Hobson

BAMBI: blind accelerated multimodal Bayesian inference

In this paper we present an algorithm for rapid Bayesian analysis that combines the benefits of nested sampling and artificial neural networks. The blind accelerated multimodal Bayesian inference (BAMBI) algorithm implements the MultiNest package for nested sampling as well as the training of an artificial neural network (NN) to learn the likelihood function. In the case of computationally expensive likelihoods, this allows the substitution of a much more rapid approximation in order to increase significantly the speed of the analysis. We begin by demonstrating, with a few toy examples, the ability of a NN to learn complicated likelihood surfaces. BAMBIs ability to decrease running time for Bayesian inference is then demonstrated in the context of estimating cosmological parameters from Wilkinson Microwave Anisotropy Probe and other observations. We show that valuable speed increases are achieved in addition to obtaining NNs trained on the likelihood functions for the different model and data combinations. These NNs can then be used for an even faster follow-up analysis using the same likelihood and different priors. This is a fully general algorithm that can be applied, without any pre-processing, to other problems with computationally expensive likelihood functions.

A simple and robust method for automated photometric classification of supernovae using neural networks

A method is presented for automated photometric classificat ion of supernovae (SNe) as TypeIa or non-Ia. A two-step approach is adopted in which: (i) the SN lightcurve flux measurements in each observing filter are fitted separately to an anal ytical parameterised function that is sufficiently flexible to accommodate vitrually all types o f SNe; and (ii) the fitted function parameters and their associated uncertainties, along with the number of flux measurements, the maximum-likelihood value of the fit and Bayesian evidenc e for the model, are used as the input feature vector to a classification neural network ( NN) that outputs the probability that the SN under consideration is of Type-Ia. The method is trained and tested using data released following the SuperNova Photometric Classificati on Challenge (SNPCC), consisting of lightcurves for 21,319 SNe in total. We consider several r andom divisions of the data into training and testing sets: for instance, for our sample D1 (D4), a total of 10 (40) per cent of the data are involved in training the algorithm and the remai nder used for blind testing of the resulting classifier; we make no selection cuts. Assigning a canonical threshold probability of pth = 0.5 on the network output to class a SN as Type-Ia, for the sample D1 (D4) we obtain a completeness of 0.78 (0.82), purity of 0.77 (0.82), an d SNPCC figure-of-merit of 0.41 (0.50). Including the SN host-galaxy redshift and its uncer tainty as additional inputs to the classification network results in a modest 5‐10 per cent incr ease in these values. We find that the quality of the classification does not vary significantly with SN redshift. Moreover, our probabilistic classification method allows one to calculat e the expected completeness, purity and figure-of-merit (or other measures of classification qua lity) as a function of the threshold probability pth, without knowing the true classes of the SNe in the testing sample, as is the case in the classification of real SNe data. The method may thus be improved further by optimising pth and can easily be extended to divide non-Ia SNe into their different classes.

Bayesian analysis of weak gravitational lensing and Sunyaev-Zel'dovich data for six galaxy clusters

We present an analysis of observations made with the Arcminute Microkelvin Imager (AMI) and the Canada–France–Hawaii Telescope (CFHT) of six galaxy clusters in a redshift range of 0.16–0.41. The cluster gas is modelled using the Sunyaev–Zel’dovich (SZ) data provided by AMI, while the total mass is modelled using the lensing data from the CFHT. In this paper, we (i) find very good agreement between SZ measurements (assuming large-scale virialization and a gas-fraction prior) and lensing measurements of the total cluster masses out to r200; (ii) perform the first multiple-component weak-lensing analysis of A115; (iii) confirm the unusual separation between the gas and mass components in A1914 and (iv) jointly analyse the SZ and lensing data for the relaxed cluster A611, confirming our use of a simulation-derived mass–temperature relation for parametrizing measurements of the SZ effect.

Bayesian constraints on dark matter halo properties using gravitationally lensed supernovae

Theoretical and observational cosmology have enjoyed a number of significant successes over the last two decades. Cosmic microwave background measurements from the Wilkinson Microwave Anisotropy Probe and Planck, together with large-scale structure and supernova (SN) searches, have put very tight constraints on cosmological parameters. Type Ia supernovae (SNIa) played a central role in the discovery of the accelerated expansion of the Universe, recognised by the Nobel Prize in Physics in 2011.The last decade has seen an enormous increase in the amount of high quality SN observations, with SN catalogues now containing hundreds of objects. This number is expected to increase to thousands in the next few years, as data from next-generation missions, such as the Dark Energy Survey and Large Synoptic Survey Telescope become available. In order to exploit the vast amount of forthcoming high quality data, it is extremely important to develop robust and efficient statistical analysis methods to answer cosmological questions, most notably determining the nature of dark energy.To address these problems my work is based on nested-sampling approaches to parameter estimation and model selection and neural networks for machine-learning. Using advanced Bayesian techniques, I constrain the properties of dark-matter haloes along the SN lines-of-sight via their weak gravitational lensing effects, develop methods for classifying SNe photometrically from their lightcurves, and present results on more general issues associated with constraining cosmological parameters and testing the consistency of different SN compilations.

Detailed SZ study of 19 LoCuSS galaxy clusters: masses and temperatures out to the virial radius

We present 16-GHz AMI SZ observations of 19 clusters with L_X >7x10^37 W (h50=1) selected from the LoCuS survey (0.142<z<0.295) and of A1758b, in the FoV of A1758a. We detect 17 clusters with 5-23sigma peak surface brightnesses. Cluster parameters are obtained using a Bayesian cluster analysis. We fit isothermal beta-models to our data and assume the clusters are virialized (with all the kinetic energy in gas internal energy). Our gas temperature, T_AMI, is derived from AMI SZ data, not from X-ray spectroscopy. Cluster parameters internal to r500 are derived assuming HSE. We find: (i) Different gNFW parameterizations yield significantly different parameter degeneracies. (ii) For h70 = 1, we find the virial radius r200 to be typically 1.6+/-0.1 Mpc and the total mass M_T(r200) typically to be 2.0-2.5xM_T(r500).(iii) Where we have found M_T X-ray (X) and weak-lensing (WL) values in the literature, there is good agreement between WL and AMI estimates (with M_{T,AMI}/M_{T,WL} =1.2^{+0.2}_{-0.3} and =1.0+/-0.1 for r500 and r200, respectively). In comparison, most Suzaku/Chandra estimates are higher than for AMI (with M_{T,X}/M_{T,AMI}=1.7+/-0.2 within r500), particularly for the stronger mergers.(iv) Comparison of T_AMI to T_X sheds light on high X-ray masses: even at large r, T_X can substantially exceed T_AMI in mergers. The use of these higher T_X values will give higher X-ray masses. We stress that large-r T_SZ and T_X data are scarce and must be increased. (v) Despite the paucity of data, there is an indication of a relation between merger activity and SZ ellipticity. (vi) At small radius (but away from any cooling flow) the SZ signal (and T_AMI) is less sensitive to ICM disturbance than the X-ray signal (and T_X) and, even at high r, mergers affect n^2-weighted X-ray data more than n-weighted SZ, implying significant shocking or clumping or both occur even in the outer parts of mergers.

A blind detection of a large, complex, Sunyaev–Zel’dovich structure★

We present an interesting Sunyaev–Zel’dovich (SZ) detection in the first of the Arcminute Microkelvin Imager (AMI) ‘blind’, degree-square fields to have been observed down to our target sensitivity of 100µJy beam^(-1). In follow-up deep pointed observations the SZ effect is detected with a maximum peak decrement greater than eight times the thermal noise. No corresponding emission is visible in the ROSAT all-sky X-ray survey and no cluster is evident in the Palomar all-sky optical survey. Compared with existing SZ images of distant clusters, the extent is large (≈10 arcmin) and complex; our analysis favours a model containing two clusters rather than a single cluster. Our Bayesian analysis is currently limited to modelling each cluster with an ellipsoidal or spherical β model, which does not do justice to this decrement. Fitting an ellipsoid to the deeper candidate we find the following. (a) Assuming that the Evrard et al. approximation to Press & Schechter correctly gives the number density of clusters as a function of mass and redshift, then, in the search area, the formal Bayesian probability ratio of the AMI detection of this cluster is 7.9 × 10^4:1; alternatively assuming Jenkins et al. as the true prior, the formal Bayesian probability ratio of detection is 2.1 × 10^5:1. (b) The cluster mass is M_(T,200) = 5.5_(-1.3)^(+1.2) x 10^(14)h^(-1)_(70) M_☉. (c) Abandoning a physical model with number density prior and instead simply modelling the SZ decrement using a phenomenological β model of temperature decrement as a function of angular distance, we find a central SZ temperature decrement of -295_(-15)^(+36) µK – this allows for cosmic microwave background primary anisotropies, receiver noise and radio sources. We are unsure if the cluster system we observe is a merging system or two separate clusters.

AMI SZ observations and Bayesian analysis of a sample of six redshift-one clusters of galaxies

We present 16-GHz Sunyaev–Zel’dovich observations using the Arcminute Microkelvin Imager (AMI) and subsequent Bayesian analysis of six galaxy clusters at redshift z ≈ 1 chosen from an X-ray- and infrared-selected sample from Culverhouse et al. In the subsequent analysis, we use two cluster models, an isothermal β-model and a Dark Matter Generalised Navarro-Frenk-White (DM-GNFW) model in order to derive a formal detection probability and the cluster parameters. We detect two clusters (CL J1415+3612 and XMJ 0830+5241) and measure their total masses out to a radius of 200 times the critical density at the respective clusters redshift. For CL J1415+3612, we find M_(T, 200) = 7.3^(+1.8)_(−1.8) × 10^(14) M_⊙ (β-model) and M_(T, 200) = 10.4^(2.5)_(−2.4) × 10^(14) M_⊙ (DM-GNFW model) and for XMJ0830+5241, we find M_(T, 200) = 3.6^(+1.1)_(−1.1) × 10^(14) M_⊙, (β-model) and M_(T, 200) = 4.7^(+1.4)_(−1.4) × 10^(14) M_⊙ (DM-GNFW model), which agree with each other for each cluster. We also present maps before and after source subtraction of the entire sample and provide 1D and 2D posterior marginalized probability distributions for each fitted cluster profile parameter of the detected clusters. Using simulations which take into account the measured source environment from the AMI Large Array (LA), source confusion noise, cosmic microwave background primordials, instrument noise, we estimate from small-radius (r_(2500)) X-ray data from Culverhouse et al., the detectability of each cluster in the sample and compare it with the result from the Small Array (SA) data. Furthermore, we discuss the validity of the assumptions of isothermality and constant gas mass fraction. We comment on the bias that these small-radius estimates introduce to large-radius SZ predictions. In addition, we follow-up the two detections with deep, single-pointed LA observations. We find a 3σ tentative decrement towards CL J1415+3612 at high resolution and a 5σ high-resolution decrement towards XM J0830+5241.

Weak lensing by triaxial galaxy clusters

ABSTRACT Weak gravitational lensing studies of galaxy clusters often assume a spherical clustermodel to simplify the analysis, but some recent studies have suggested this simplifying as-sumption may result in large biases in estimated cluster masses and concentration values,since clusters are expected to exhibit triaxiality. Several such analyses have, however, quotedexpressions for the spatial derivatives of the lensing potential in triaxial models, which areopen to misinterpretation.In this paper, we give a clear description of weak lensing by triaxialNFW galaxy clusters and also present an efficient and robust m ethod to model these clustersand obtain parameter estimates. By considering four highly triaxial NFW galaxy clusters, were-examine the impact of simplifying spherical assumptions and found that while the concen-tration estimates are largely unbiased except in one of our traixial NFW simulated clusters,for which the concentration is only slightly biased, the masses are significantly biased, by upto 40%, for all the clusters we analysed. Moreover, we find that such assumptions can leadto the erroneous conclusion that some substructure is present in the galaxy clusters or, evenworse, that multiple galaxy clusters are present in the field . Our cluster fitting method alsoallows one to answer the question of whether a given cluster exhibits triaxiality or a simplespherical model is good enough.Key words: methods: data analysis – methods: statistical – cosmology: observations – galax-ies: clusters: general