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Priors in Bayesian analyses often encode informative domain knowledge that can be useful in making the inference process more efficient. Occasionally, however, priors may be unrepresentative of the parameter values for a given dataset, which can result in inefficient parameter space exploration, or even incorrect inferences, particularly for nested sampling (NS) algorithms. Simply broadening the prior in such cases may be inappropriate or impossible in some applications. Hence our previous solution to this problem, known as posterior repartitioning (PR), redefines the prior and likelihood while keeping their product fixed, so that the posterior inferences and evidence estimates remain unchanged, but the efficiency of the NS process is significantly increased. In its most practical form, PR raises the prior to some power beta, which is introduced as an auxiliary variable that must be determined on a case-by-case basis, usually by lowering beta from unity according to some pre-defined `annealing schedule' until the resulting inferences converge to a consistent solution. Here we present a very simple yet powerful alternative Bayesian approach, in which beta is instead treated as a hyperparameter that is inferred from the data alongside the original parameters of the problem, and then marginalised over to obtain the final inference. We show through numerical examples that this Bayesian PR (BPR) method provides a very robust, self-adapting and computationally efficient `hands-off' solution to the problem of unrepresentative priors in Bayesian inference using NS. Moreover, unlike the original PR method, we show that even for representative priors BPR has a negligible computational overhead relative to standard nesting sampling, which suggests that it should be used as the default in all NS analyses.

We present CARMA observations of a massive galaxy cluster discovered in the AMI blind SZ survey. Without knowledge of the cluster redshift a Bayesian analysis of the AMI, CARMA and joint AMI & CARMA uv-data is used to quantify the detection significance and parameterise both the physical and observational properties of the cluster whilst accounting for the statistics of primary CMB anisotropies, receiver noise and radio sources. The joint analysis of the AMI & CARMA uv-data was performed with two parametric physical cluster models: the ��-model; and the model described in Olamaie et al. 2012 with the pressure profile fixed according to Arnaud et al. 2010. The cluster mass derived from these different models is comparable but our Bayesian evidences indicate a preference for the ��-profile which we, therefore, use throughout our analysis. From the CARMA data alone we obtain a Bayesian probability of detection ratio of 12.8:1 when assuming that a cluster exists within our search area; alternatively assuming that Jenkins et al. 2001 accurately predicts the number of clusters as a function of mass and redshift, the Bayesian probability of detection is 0.29:1. From the analysis of the AMI or AMI & CARMA data the probability of detection ratio exceeds 4.5x10^3:1. Performing a joint analysis of the AMI & CARMA data with a physical cluster model we derive the total mass internal to r200 as MT,200 = 4.1x10^14Msun. Using a phenomenological ��-model to quantify the temperature decrement as a function of angular distance we find a central SZ temperature decrement of 170��K in the AMI & CARMA data. The SZ decrement in the CARMA data is weaker than expected and we speculate that this is a consequence of the cluster morphology. In a forthcoming study we will assess the impact of cluster morphology on the SZ decrements that are observed with interferometers such as AMI and CARMA., 13 pages, 13 figures, 6 tables. Accepted by MNRAS

GJ667C is the least massive component of a triple star system which lies at a distance of about 6.8 pc (22.1 light-years) from 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 over-estimated 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 timescale for HARPS data of order 9 days. Our analysis shows that the data only provides strong evidence for the presence of two planets: GJ667Cb and c with periods 7.19d and 28.13d respectively, with some hints towards the presence of a third signal with period 91d. 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 under-estimated at the level of ~50 per cent., Comment: 10 pages, 6 figures, 3 tables, accepted for publication in MNRAS. Some minor changes in response to referee's comments. arXiv admin note: substantial text overlap with arXiv:1012.5129

We have obtained deep SZ observations towards 15 of the apparently hottest XMM Cluster Survey (XCS) clusters that can be observed with the Arcminute Microkelvin Imager (AMI). We use a Bayesian analysis to quantify the significance of our SZ detections. We detect the SZ effect at high significance towards three of the clusters and at lower significance for a further two clusters. Towards the remaining ten clusters, no clear SZ signal was measured. We derive cluster parameters using the XCS mass estimates as a prior in our Bayesian analysis. For all AMI-detected clusters, we calculate large-scale mass and temperature estimates while for all undetected clusters we determine upper limits on these parameters. We find that the large- scale mean temperatures derived from our AMI SZ measurements (and the upper limits from null detections) are substantially lower than the XCS-based core-temperature estimates. For clusters detected in the SZ, the mean temperature is, on average, a factor of 1.4 lower than temperatures from the XCS. For clusters undetected in SZ, the average 68% upper limit on the mean temperature is a factor of 1.9 below the XCS temperature., Comment: 18 pages, 14 figures, 6 tables. Accepted by MNRAS

We present 16-GHz Sunyaev-Zel'dovich observations using the Arcminute Microkelvin Imager (AMI) and subsequent Bayesian analysis of six galaxy clusters at redshift ($z \approx 1$) chosen from an X-ray and Infrared selected sample from Culverhouse et al. (2010). In the subsequent analysis we use two cluster models, an isothermal ��-model and a Dark Matter GNFW (DM-GNFW) model in order to derive a formal detection probability and the cluster parameters. We detect two clusters (CLJ1415+3612 & XMJ0830+5241) and measure their total masses out to a radius of 200 $\times$ the critical density at the respective cluster's redshift. For CLJ1415+3612 and XMJ0830+5241, we find M_{\mathrm{T},200} for each 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 marginalised 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, CMB primordials, instrument noise, we estimate from low-radius X-ray data from Culverhouse et al. (2010), 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 3 sigma tentative decrement toward CLJ1415+3612 at high-resolution and a 5 sigma high-resolution decrement towards XMJ0830+5241., 11 pages, 10 figures, accepted by Monthly Notices of the Royal Astronomical Society

We present 16-GHz observations using the Arcminute Microkelvin Imager (AMI) of 11 clusters with 7 x 10^{37}W < L_X < 11 x 10^{37}W (h_{50}=1.0) selected from the Local Cluster Substructure Survey (LoCuSS) and compare them to X-ray data. We use a fast, Bayesian cluster analysis to explore the high-dimensional parameter space of the cluster-plus-sources model and obtain robust cluster parameter estimates in the presence of radio point sources, receiver noise and primordial CMB anisotropy. Our analysis fits a spherical, isothermal beta-model to our data and assumes the cluster follows the theoretical mass-temperature relation. Large-scale cluster parameters internal to r_{500} are derived under the assumption of hydrostatic equilibrium. Posterior distributions for the large-scale parameters of 8 of our clusters are given; SZ effects towards Abell 1704 and Zw0857.9+2107 were not detected and our spherical beta-profile was found to be an inadequate fit to the decrement on our map for Abell 2409., 17 pages, 12 figures, 4 tables This paper has been withdrawn by the authors due to major changes

We present observations from the Small Array of the Arcminute Microkelvin Imager (AMI) of eight high X-ray luminosity galaxy cluster systems selected from the Local Cluster Substructure Survey (LoCuSS) sample.We detect the Sunyaev-Zel'dovich (SZ) effect in seven of these clusters. With the assumptions that galaxy clusters are isothermal, have a density profile described by a spherical b -model and obey the theoretical M-T relation, we are able to derive cluster parameters at r200 from our SZ data. With the additional assumption of hydrostatic equilibrium we are able to derive parameters at r500. We present posterior probability distributions for cluster parameters such as mass, radius and temperature (TSZ, MT). Combining our sample with that of AMI Consortium: Rodr'\iguez-Gonz\'alvez et al. (2011) and using large-radius X-ray temperature estimates (TX) from Chandra and Suzaku observations, we find that there is reasonable correspondence between TX and TSZ,MT values at low TX, but that for clusters with TX above around 6keV the correspondence breaks down with TX exceeding TSZ, MT; we stress that this finding is based on just ten clusters., Comment: 17 pages, 4 tables, 14 figures

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. BAMBI's 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., Comment: 12 pages, 8 tables, 17 figures; accepted by MNRAS; v2 to reflect minor changes in published version

We present observations using the Small Array of the Arcminute Microkelvin Imager (AMI; 14-18 GHz) of four Abell and three MACS clusters spanning 0.171-0.686 in redshift. We detect Sunyaev-Zel'dovich (SZ) signals in five of these without any attempt at source subtraction, although strong source contamination is present. With radio-source measurements from high-resolution observations, and under the assumptions of spherical $\beta$-model, isothermality and hydrostatic equilibrium, a Bayesian analysis of the data in the visibility plane detects extended SZ decrements in all seven clusters over and above receiver noise, radio sources and primary CMB imprints. Bayesian evidence ratios range from 10^{11}:1 to 10^{43}:1 for six of the clusters and 3000:1 for one with substantially less data than the others. We present posterior probability distributions for, e.g., total mass and gas fraction averaged over radii internal to which the mean overdensity is 1000, 500 and 200, r_200 being the virial radius. Reaching r_200 involves some extrapolation for the nearer clusters but not for the more-distant ones. We find that our estimates of gas fraction are low (compared with most in the literature) and decrease with increasing radius. These results appear to be consistent with the notion that gas temperature in fact falls with distance (away from near the cluster centre) out to the virial radius., Comment: 18 pages, 10 figures, submitted to MNRAS (updated authors and fixed Figure 1)

Most Sunyaev--Zel'dovich (SZ) and X-ray analyses of galaxy clusters try to constrain the cluster total mass and/or gas mass using parameterised models and assumptions of spherical symmetry and hydrostatic equilibrium. By numerically exploring the probability distributions of the cluster parameters given the simulated interferometric SZ data in the context of Bayesian methods, and assuming a beta-model for the electron number density we investigate the capability of this model and analysis to return the simulated cluster input quantities via three rameterisations. In parameterisation I we assume that the T is an input parameter. We find that parameterisation I can hardly constrain the cluster parameters. We then investigate parameterisations II and III in which fg(r200) replaces temperature as a main variable. In parameterisation II we relate M_T(r200) and T assuming hydrostatic equilibrium. We find that parameterisation II can constrain the cluster physical parameters but the temperature estimate is biased low. In parameterisation III, the virial theorem replaces the hydrostatic equilibrium assumption. We find that parameterisation III results in unbiased estimates of the cluster properties. We generate a second simulated cluster using a generalised NFW (GNFW) pressure profile and analyse it with an entropy based model to take into account the temperature gradient in our analysis and improve the cluster gas density distribution. This model also constrains the cluster physical parameters and the results show a radial decline in the gas temperature as expected. The mean cluster total mass estimates are also within 1 sigma from the simulated cluster true values. However, we find that for at least interferometric SZ analysis in practice at the present time, there is no differences in the AMI visibilities between the two models. This may of course change as the instruments improve., Comment: 19 pages, 13 tables, 24 figures