ALBERT

Description: A method is presented for Bayesian model selection without explicitly computing evidences, by using a combined likelihood and introducing an integer model selection parameter n so that Bayes factors, or more generally posterior odds ratios, may be read off directly from the posterior of n . If the total number of models under consideration is specified a priori , the full joint parameter space (, n ) of the models is of fixed dimensionality and can be explored using standard Markov chain Monte Carlo (MCMC) or nested sampling methods, without the need for reversible jump MCMC techniques. The posterior on n is then obtained by straightforward marginalization. We demonstrate the efficacy of our approach by application to several toy models. We then apply it to constraining the dark energy equation of state using a free-form reconstruction technique. We show that cold dark matter is significantly favoured over all extensions, including the simple w ( z ) = constant model.

Description: Using Arcminute Microkelvin Imager (AMI) Sunyaev–Zel'dovich (SZ) observations towards 10 CLASH (Cluster Lensing and Supernova Survey with Hubble) clusters, we investigate the influence of cluster mergers on observational galaxy cluster studies. Although selected to be largely relaxed, there is disagreement in the literature on the dynamical states of CLASH sample members. We analyse our AMI data in a fully Bayesian way to produce estimated cluster parameters and consider the intrinsic correlations in our Navarro, Frenk and White/generalized Navarro, Frenk and White-based model. Varying pressure profile shape parameters, illustrating an influence of mergers on scaling relations, induces small deviations from the canonical self-similar predictions – in agreement with simulations of Poole et al. ( 2007 ) who found that merger activity causes only small scatter perpendicular to the relations. We demonstrate this effect observationally using the different dependences of SZ and X-ray signals to n e that cause different sensitivities to the shocking and/or fractionation produced by mergers. Plotting Y X – M gas relations (where Y X = M gas T ) derived from AMI SZ and from Chandra X-ray gives ratios of AMI and Chandra Y X and M gas estimates that indicate movement of clusters along the scaling relation, as predicted by Poole et al. ( 2007 ). Clusters that have moved most along the relation have the most discrepant T SZ and T X estimates: all the other clusters (apart from one) have SZ and X-ray estimates of M gas , T and Y X that agree within r 500 . We use SZ versus X-ray discrepancies in conjunction with Chandra maps and T X profiles, making comparisons with simulated cluster merger maps in Poole et al. ( 2006 ) to identify disturbed members of our sample and estimate merger stages.

Description: The R h  =  ct cosmological model has received considerable attention in recent years owing to claims that it is favoured over the standard cold dark mater (CDM) model by most observational data. A key feature of the R h  =  ct model is that the zero active mass condition  + 3 p  = 0 holds at all epochs. Most recently, Melia has claimed that this condition is a requirement of the symmetries of the Friedmann–Robertson–Walker spacetime. We demonstrate that this claim is false and results from a flaw in the logic of Melia's argument.

Description: We extend the Kolmogorov–Smirnov (K–S) test to multiple dimensions by suggesting a $\mathbb {R}^n \rightarrow [0,1]$ mapping based on the probability content of the highest probability density region of the reference distribution under consideration; this mapping reduces the problem back to the one-dimensional case to which the standard K–S test may be applied. The universal character of this mapping also allows us to introduce a simple, yet general, method for the validation of Bayesian posterior distributions of any dimensionality. This new approach goes beyond validating software implementations; it provides a sensitive test for all assumptions, explicit or implicit, that underlie the inference. In particular, the method assesses whether the inferred posterior distribution is a truthful representation of the actual constraints on the model parameters. We illustrate our multidimensional K–S test by applying it to a simple two-dimensional Gaussian toy problem, and demonstrate our method for posterior validation in the real-world astrophysical application of estimating the physical parameters of galaxy clusters parameters from their Sunyaev–Zel'dovich effect in microwave background data. In the latter example, we show that the method can validate the entire Bayesian inference process across a varied population of objects for which the derived posteriors are different in each case.

Description: 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/ .

Description: 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/ .

Description: 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/ .

Description: We introduce a method for performing a robust Bayesian analysis of non-Gaussianity present in pulsar timing data, simultaneously with the pulsar timing model, and additional stochastic parameters such as those describing red spin noise and dispersion measure variations. The parameters used to define the presence of non-Gaussianity are zero for Gaussian processes, giving a simple method of defining the strength of non-Gaussian behaviour. We use simulations to show that assuming Gaussian statistics when the noise in the data is drawn from a non-Gaussian distribution can significantly increase the uncertainties associated with the pulsar timing model parameters. We then apply the method to the publicly available 15 yr Parkes Pulsar Timing Array data release 1 data set for the binary pulsar J0437–4715. In this analysis, we present a significant detection of non-Gaussianity in the uncorrelated non-thermal noise, but we find that it does not yet impact the timing model or stochastic parameter estimates significantly compared to analysis performed assuming Gaussian statistics. The methods presented are, however, shown to be of immediate practical use for current European Pulsar Timing Array and International Pulsar Timing Array data sets.

Description: We present the first public release of our Bayesian inference tool, bayes-x , for the analysis of X-ray observations of galaxy clusters. We illustrate the use of bayes-x by analysing a set of four simulated clusters at z = 0.2–0.9 as they would be observed by a Chandra -like X-ray observatory. In both the simulations and the analysis pipeline we assume that the dark matter density follows a spherically symmetric Navarro, Frenk and White (NFW) profile and that the gas pressure is described by a generalized NFW (GNFW) profile. We then perform four sets of analyses. These include prior-only analyses and analyses in which we adopt wide uniform prior probability distributions on f g ( r 200 ) and on the model parameters describing the shape and slopes of the GNFW pressure profile, namely ( c 500 , a , b , c ). By numerically exploring the joint probability distribution of the cluster parameters given simulated Chandra -like data, we show that the model and analysis technique can robustly return the simulated cluster input quantities, constrain the cluster physical parameters and reveal the degeneracies among the model parameters and cluster physical parameters. We then use bayes-x to analyse Chandra data on the nearby cluster, A262, and derive the cluster physical and thermodynamic profiles. The results are in good agreement with other results given in literature for the cluster. To illustrate the performance of the Bayesian model selection, we also carried out analyses assuming an Einasto profile for the matter density and calculated the Bayes factor. The results of the model selection analyses for the simulated data favour the NFW model as expected. However, we find that the Einasto profile is preferred in the analysis of A262. The bayes-x software, which is implemented in Fortran 90, is available at http://www.mrao.cam.ac.uk/facilities/software/bayesx/ .

Description: It is now common practice to constrain cosmological parameters using supernovae (SNe) catalogues constructed from several different surveys. Before performing such a joint analysis, however, one should check that parameter constraints derived from the individual SNe surveys that make up the catalogue are mutually consistent. We describe a statistically-robust mutual consistency test, which we calibrate using simulations, and apply it to each pairwise combination of the large surveys making up, respectively, the UNION2 catalogue and the very recent JLA (joint light-curve analysis) compilation by Betoule et al. We find no inconsistencies in the latter case, but conclusive evidence for inconsistency between some survey pairs in the UNION2 catalogue.