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

D-optimal designs via a cocktail algorithm

A fast new algorithm is proposed for numerical computation of (approximate) D-optimal designs. This "cocktail algorithm" extends the well-known vertex direction method (VDM; Fedorov 1972) and the multiplicative algorithm (Silvey, Titterington and Torsney, 1978), and shares their simplicity and monotonic convergence properties. Numerical examples show that the cocktail algorithm can lead to dramatically improved speed, sometimes by orders of magnitude, relative to either the multiplicative algorithm or the vertex exchange method (a variant of VDM). Key to the improved speed is a new nearest neighbor exchange strategy, which acts locally and complements the global effect of the multiplicative algorithm. Possible extensions to related problems such as nonparametric maximum likelihood estimation are mentioned.Comment: A number of changes after accounting for the referees' comments including new examples in Section 4 and more detailed explanations throughou

Mixture modeling with applications in schizophrenia research

Finite mixture modeling, together with the EM algorithm, have been widely used in clustering analysis. Under such methods, the unknown group membership is usually treated as missing data. When the "complete data" (log-)likelihood function does not have an explicit solution, the simplicity of the EM algorithm breaks down. Authors, including Rai and Matthews (1993), Lange (1995a) and Titterington (1984), developed modified algorithms therefore. As motivated by research in a large neurobiological project, we propose in this paper a new variant of such modifications and show that it is self-consistent. Moreover, simulations are conducted to demonstrate that the new variant converges faster than its predecessors. Originally published Computational Statistics and Data Analysis, Vol. 53, No. 7, May 200

Scattering statistics of rock outcrops: Model-data comparisons and Bayesian inference using mixture distributions

The probability density function of the acoustic field amplitude scattered by the seafloor was measured in a rocky environment off the coast of Norway using a synthetic aperture sonar system, and is reported here in terms of the probability of false alarm. Interpretation of the measurements focused on finding appropriate class of statistical models (single versus two-component mixture models), and on appropriate models within these two classes. It was found that two-component mixture models performed better than single models. The two mixture models that performed the best (and had a basis in the physics of scattering) were a mixture between two K distributions, and a mixture between a Rayleigh and generalized Pareto distribution. Bayes' theorem was used to estimate the probability density function of the mixture model parameters. It was found that the K-K mixture exhibits significant correlation between its parameters. The mixture between the Rayleigh and generalized Pareto distributions also had significant parameter correlation, but also contained multiple modes. We conclude that the mixture between two K distributions is the most applicable to this dataset.Comment: 15 pages, 7 figures, Accepted to the Journal of the Acoustical Society of Americ

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

A detailed radio study of the energetic, nearby, and puzzling GRB 171010A

We present the results of an intensive multi-epoch radio frequency campaign on the energetic and nearby GRB 171010A with the Karl G. Janksy Very Large Array and Arcminute Microkelvin Imager Large Array. We began observing GRB 171010A a day after its initial detection, and were able to monitor the temporal and spectral evolution of the source over the following weeks. The spectra and their evolution are compared to the canonical theories for broadband GRB afterglows, with which we find a general agreement. There are, however, a number of features that are challenging to explain with a simple forward shock model, and we discuss possible reasons for these discrepancies. This includes the consideration of the existence of a reverse shock component, potential microphysical parameter evolution and the effect of scintillation

Cosmological parameter estimation using Very Small Array data out to ℓ= 1500

We estimate cosmological parameters using data obtained by the Very Small Array (VSA) in its extended configuration, in conjunction with a variety of other cosmic microwave background (CMB) data and external priors. Within the flat Λ cold dark matter (ΛCDM) model, we find that the inclusion of high-resolution data from the VSA modifies the limits on the cosmological parameters as compared to those suggested by the Wilkinson Microwave Anisotropy Probe (WMAP) alone, while still remaining compatible with their estimates. We find that Ωbh2= 0.0234+0.0012−0.0014, Ωdmh2= 0.111+0.014−0.016, h= 0.73+0.09−0.05, nS= 0.97+0.06−0.03, 1010AS= 23+7−3 and τ= 0.14+0.14−0.07 for WMAP and VSA when no external prior is included. On extending the model to include a running spectral index of density fluctuations, we find that the inclusion of VSA data leads to a negative running at a level of more than 95 per cent confidence ( nrun=−0.069 ± 0.032 ), something that is not significantly changed by the inclusion of a stringent prior on the Hubble constant. Inclusion of prior information from the 2dF galaxy redshift survey reduces the significance of the result by constraining the value of Ωm. We discuss the veracity of this result in the context of various systematic effects and also a broken spectral index model. We also constrain the fraction of neutrinos and find that fν < 0.087 at 95 per cent confidence, which corresponds to mν < 0.32 eV when all neutrino masses are equal. Finally, we consider the global best fit within a general cosmological model with 12 parameters and find consistency with other analyses available in the literature. The evidence for nrun < 0 is only marginal within this model

Quantitative assessment of sewer overflow performance with climate change in northwest England

Changes in rainfall patterns associated with climate change can affect the operation of a combined sewer system, with the potential increase in rainfall amount. This could lead to excessive spill frequencies and could also introduce hazardous substances into the receiving waters, which, in turn, would have an impact on the quality of shellfish and bathing waters. This paper quantifies the spilling volume, duration and frequency of 19 combined sewer overflows (CSOs) to receiving waters under two climate change scenarios, the high (A1FI), and the low emissions (B1) scenarios, simulated by three global climate models (GCMs), for a study catchment in northwest England. The future rainfall is downscaled, using climatic variables from HadCM3, CSIRO and CGCM2 GCMs, with the use of a hybrid generalized linear–artificial neural network model. The results from the model simulation for the future in 2080 showed an annual increase of 37% in total spill volume, 32% in total spill duration, and 12% in spill frequency for the shellfish water limiting requirements. These results were obtained, under the high emissions scenario, as projected by the HadCM3 as maximum. Nevertheless, the catchment drainage system is projected to cope with the future conditions in 2080 by all three GCMs. The results also indicate that under scenario B1, a significant drop was projected by CSIRO, which in the worst case could reach up to 50% in spill volume, 39% in spill duration and 25% in spill frequency. The results further show that, during the bathing season, a substantial drop is expected in the CSO spill drivers, as predicted by all GCMs under both scenarios

Millihertz X-ray variability during the 2019 outburst of black hole candidate Swift~J1357.2−-0933

Swift J1357.2$-$0933 is a black-hole candidate X-ray transient, which underwent its third outburst in 2019, during which several multi-wavelength observations were carried out.~Here, we report results from the \emph{Neil Gehrels Swift} and \emph{NICER} observatories and radio data from \emph{AMI}.~For the first time,~millihertz quasi-periodic X-ray oscillations with frequencies varying between ${\sim}$~1--5~$\rm{mHz}$ were found in \emph{NICER} observations and a similar feature was also detected in one \emph{Swift}--\textsc{XRT} dataset.~Our spectral analysis indicate that the maximum value of the measured X-ray flux is much lower compared to the peak values observed during the 2011 and 2017 outbursts.~This value is ${\sim}$~100 times lower than found with \emph{MAXI} on MJD~58558 much ($\sim$~68 days) earlier in the outburst, suggesting that the \emph{Swift} and \emph{NICER} fluxes belong to the declining phase of the 2019 outburst.~An additional soft component was detected in the \textsc{XRT} observation with the highest flux level, but at a relatively low $L_{\rm X}$~$\sim$~$3{\times}10^{34}~(d/{\rm 6~kpc)}^2\rm{erg}~\rm{s}^{-1}$, and which we fitted with a disc component at a temperature of $\sim 0.17$~keV.~The optical/UV magnitudes obtained from \emph{Swift}--\textsc{UVOT} showed a correlation with X-ray observations, indicating X-ray reprocessing to be the plausible origin of the optical and UV emission.~However, the source was not significantly detected in the radio band.~There are currently a number of models that could explain this millihertz-frequency X-ray variability; not least of which involves an X-ray component to the curious dips that, so far, have only been observed in the optical.Comment: 14 pages, Accepted for publication in MNRA

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