Hierarchical Gaussian process mixtures for regression

As a result of their good performance in practice and their desirable analytical properties, Gaussian process regression models are becoming increasingly of interest in statistics, engineering and other fields. However, two major problems arise when the model is applied to a large data-set with repeated measurements. One stems from the systematic heterogeneity among the different replications, and the other is the requirement to invert a covariance matrix which is involved in the implementation of the model. The dimension of this matrix equals the sample size of the training data-set. In this paper, a Gaussian process mixture model for regression is proposed for dealing with the above two problems, and a hybrid Markov chain Monte Carlo (MCMC) algorithm is used for its implementation. Application to a real data-set is reported

A Bayesian reassessment of nearest-neighbour classification

The k-nearest-neighbour procedure is a well-known deterministic method used in supervised classification. This paper proposes a reassessment of this approach as a statistical technique derived from a proper probabilistic model; in particular, we modify the assessment made in a previous analysis of this method undertaken by Holmes and Adams (2002,2003), and evaluated by Manocha and Girolami (2007), where the underlying probabilistic model is not completely well-defined. Once a clear probabilistic basis for the k-nearest-neighbour procedure is established, we derive computational tools for conducting Bayesian inference on the parameters of the corresponding model. In particular, we assess the difficulties inherent to pseudo-likelihood and to path sampling approximations of an intractable normalising constant, and propose a perfect sampling strategy to implement a correct MCMC sampler associated with our model. If perfect sampling is not available, we suggest using a Gibbs sampling approximation. Illustrations of the performance of the corresponding Bayesian classifier are provided for several benchmark datasets, demonstrating in particular the limitations of the pseudo-likelihood approximation in this set-up

An approximate Bayesian marginal likelihood approach for estimating finite mixtures

Estimation of finite mixture models when the mixing distribution support is unknown is an important problem. This paper gives a new approach based on a marginal likelihood for the unknown support. Motivated by a Bayesian Dirichlet prior model, a computationally efficient stochastic approximation version of the marginal likelihood is proposed and large-sample theory is presented. By restricting the support to a finite grid, a simulated annealing method is employed to maximize the marginal likelihood and estimate the support. Real and simulated data examples show that this novel stochastic approximation--simulated annealing procedure compares favorably to existing methods.Comment: 16 pages, 1 figure, 3 table

AMI-LA Observations of the SuperCLASS Super-cluster

We present a deep survey of the SuperCLASS super-cluster - a region of sky known to contain five Abell clusters at redshift $z\sim0.2$ - performed using the Arcminute Microkelvin Imager (AMI) Large Array (LA) at 15.5$~$GHz. Our survey covers an area of approximately 0.9 square degrees. We achieve a nominal sensitivity of $32.0~\mu$Jy beam$^{-1}$ toward the field centre, finding 80 sources above a $5\sigma$ threshold. We derive the radio colour-colour distribution for sources common to three surveys that cover the field and identify three sources with strongly curved spectra - a high-frequency-peaked source and two GHz-peaked-spectrum sources. The differential source count (i) agrees well with previous deep radio source count, (ii) exhibits no evidence of an emerging population of star-forming galaxies, down to a limit of 0.24$~$mJy, and (iii) disagrees with some models of the 15$~$GHz source population. However, our source count is in agreement with recent work that provides an analytical correction to the source count from the SKADS Simulated Sky, supporting the suggestion that this discrepancy is caused by an abundance of flat-spectrum galaxy cores as-yet not included in source population models.Comment: 17 pages, 14 figures, 3 tables. Accepted for publication in MNRA

Pinning down the ram-pressure-induced halt of star formation in the Virgo cluster spiral galaxy NGC 4388. A joint inversion of spectroscopic and photometric data

In a galaxy cluster, the evolution of spiral galaxies depends on their cluster environment. Ram pressure due to the rapid motion of a spiral galaxy within the hot intracluster medium removes the galaxy's interstellar medium from the outer disk. Once the gas has left the disk, star formation stops. The passive evolution of the stellar populations should be detectable in optical spectroscopy and multi-wavelength photometry. The goal of our study is to recover the stripping age of the Virgo spiral galaxy NGC 4388, i.e. the time elapsed since the halt of star formation in the outer galactic disk using a combined analysis of optical spectra and photometry. We performed VLT FORS2 long-slit spectroscopy of the inner star-forming and outer gas-free disk of NGC 4388. We developed a non-parametric inversion tool that allows us to reconstruct the star formation history of a galaxy from spectroscopy and photometry. The tool was tested on a series of mock data using Monte Carlo simulations. The results from the non-parametric inversion were refined by applying a parametric inversion method. The star formation history of the unperturbed galactic disk is flat. The non-parametric method yields a rapid decline of star formation < 200 Myr ago in the outer disk. The parametric method is not able to distinguish between an instantaneous and a long-lasting star formation truncation. The time since the star formation has dropped by a factor of two from its pre-stripping value is 190 +- 30 Myr. We are able to give a precise stripping age that is consistent with revised dynamical models.Comment: 12 pages, 10 figures, accepted for publication in A&

First results from the Very Small Array -- IV. Cosmological parameter estimation

We investigate the constraints on basic cosmological parameters set by the first compact-configuration observations of the Very Small Array (VSA), and other cosmological data sets, in the standard inflationary LambdaCDM model. Using a weak prior 40 < H_0 < 90 km/s/Mpc and 0 < tau < 0.5 we find that the VSA and COBE_DMR data alone produce the constraints Omega_tot = 1.03^{+0.12}_{-0.12}, Omega_bh^2 = 0.029^{+0.009}_{-0.009}, Omega_cdm h^2 = 0.13^{+0.08}_{-0.05} and n_s = 1.04^{+0.11}_{-0.08} at the 68 per cent confidence level. Adding in the type Ia supernovae constraints, we additionally find Omega_m = 0.32^{+0.09}_{-0.06} and Omega_Lambda = 0.71^{+0.07}_{-0.07}. These constraints are consistent with those found by the BOOMERanG, DASI and MAXIMA experiments. We also find that, by combining all the recent CMB experiments and assuming the HST key project limits for H_0 (for which the X-ray plus Sunyaev--Zel'dovich route gives a similar result), we obtain the tight constraints Omega_m=0.28^{+0.14}_{-0.07} and Omega_Lambda= 0.72^{+0.07}_{-0.13}, which are consistent with, but independent of, those obtained using the supernovae data.Comment: 10 pages, 6 figures, MNRAS in pres

High resolution AMI Large Array imaging of spinning dust sources: spatially correlated 8 micron emission and evidence of a stellar wind in L675

We present 25 arcsecond resolution radio images of five Lynds Dark Nebulae (L675, L944, L1103, L1111 & L1246) at 16 GHz made with the Arcminute Microkelvin Imager (AMI) Large Array. These objects were previously observed with the AMI Small Array to have an excess of emission at microwave frequencies relative to lower frequency radio data. In L675 we find a flat spectrum compact radio counterpart to the 850 micron emission seen with SCUBA and suggest that it is cm-wave emission from a previously unknown deeply embedded young protostar. In the case of L1246 the cm-wave emission is spatially correlated with 8 micron emission seen with Spitzer. Since the MIR emission is present only in Spitzer band 4 we suggest that it arises from a population of PAH molecules, which also give rise to the cm-wave emission through spinning dust emission.Comment: accepted MNRA