We present further development and the first public release of our multimodal nested sampling algorithm, called MultiNest. This Bayesian inference tool calculates the evidence, with an associated ...error estimate, and produces posterior samples from distributions that may contain multiple modes and pronounced (curving) degeneracies in high dimensions. The developments presented here lead to further substantial improvements in sampling efficiency and robustness, as compared to the original algorithm presented in Feroz & Hobson, which itself significantly outperformed existing Markov chain Monte Carlo techniques in a wide range of astrophysical inference problems. The accuracy and economy of the MultiNest algorithm are demonstrated by application to two toy problems and to a cosmological inference problem focusing on the extension of the vanilla Λ cold dark matter model to include spatial curvature and a varying equation of state for dark energy. The MultiNest software, which is fully parallelized using MPI and includes an interface to CosmoMC, is available at http://www.mrao.cam.ac.uk/software/multinest/. It will also be released as part of the SuperBayeS package, for the analysis of supersymmetric theories of particle physics, at http://www.superbayes.org.
In performing a Bayesian analysis of astronomical data, two difficult problems often emerge. First, in estimating the parameters of some model for the data, the resulting posterior distribution may ...be multimodal or exhibit pronounced (curving) degeneracies, which can cause problems for traditional Markov Chain Monte Carlo (MCMC) sampling methods. Secondly, in selecting between a set of competing models, calculation of the Bayesian evidence for each model is computationally expensive using existing methods such as thermodynamic integration. The nested sampling method introduced by Skilling, has greatly reduced the computational expense of calculating evidence and also produces posterior inferences as a by-product. This method has been applied successfully in cosmological applications by Mukherjee, Parkinson & Liddle, but their implementation was efficient only for unimodal distributions without pronounced degeneracies. Shaw, Bridges & Hobson recently introduced a clustered nested sampling method which is significantly more efficient in sampling from multimodal posteriors and also determines the expectation and variance of the final evidence from a single run of the algorithm, hence providing a further increase in efficiency. In this paper, we build on the work of Shaw et al. and present three new methods for sampling and evidence evaluation from distributions that may contain multiple modes and significant degeneracies in very high dimensions; we also present an even more efficient technique for estimating the uncertainty on the evaluated evidence. These methods lead to a further substantial improvement in sampling efficiency and robustness, and are applied to two toy problems to demonstrate the accuracy and economy of the evidence calculation and parameter estimation. Finally, we discuss the use of these methods in performing Bayesian object detection in astronomical data sets, and show that they significantly outperform existing MCMC techniques. An implementation of our methods will be publicly released shortly.
ABSTRACT We present the results of the most complete scan of the parameter space for cosmic ray (CR) injection and propagation. We perform a Bayesian search of the main GALPROP parameters, using the ...MultiNest nested sampling algorithm, augmented by the BAMBI neural network machine-learning package. This is the first study to separate out low-mass isotopes (p, , and He) from the usual light elements (Be, B, C, N, and O). We find that the propagation parameters that best-fit , and He data are significantly different from those that fit light elements, including the B/C and 10Be/9Be secondary-to-primary ratios normally used to calibrate propagation parameters. This suggests that each set of species is probing a very different interstellar medium, and that the standard approach of calibrating propagation parameters using B/C can lead to incorrect results. We present posterior distributions and best-fit parameters for propagation of both sets of nuclei, as well as for the injection abundances of elements from H to Si. The input GALDEF files with these new parameters will be included in an upcoming public GALPROP update.
GJ667C is the least massive component of a triple star system which lies at a distance of about 6.8 pc (22.1 light-year) from the 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 overestimated 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 time-scale for HARPS data of the order of 9 d. Our analysis shows that the data only provide strong evidence for the presence of two planets: GJ667Cb and c with periods 7.19 and 28.13 d, respectively, with some hints towards the presence of a third signal with period 91 d. 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 underestimated at the level of ∼50 per cent.
A new Bayesian software package for the analysis of pulsar timing data is presented in the form of temponest which allows for the robust determination of the non-linear pulsar timing solution ...simultaneously with a range of additional stochastic parameters. This includes both red spin noise and dispersion measure variations using either power-law descriptions of the noise, or through a model-independent method that parametrizes the power at individual frequencies in the signal. We use temponest to show that at noise levels representative of current data sets in the European Pulsar Timing Array and International Pulsar Timing Array the linear timing model can underestimate the uncertainties of the timing solution by up to an order of magnitude. We also show how to perform Bayesian model selection between different sets of timing model and stochastic parameters, for example, by demonstrating that in the pulsar B1937+21 both the dispersion measure variations and spin noise in the data are optimally modelled by simple power laws. Finally, we show that not including the stochastic parameters simultaneously with the timing model can lead to unpredictable variation in the estimated uncertainties, compromising the robustness of the scientific results extracted from such analysis.
A method is presented for automated photometric classification of supernovae (SNe) as Type Ia or non-Ia. A two-step approach is adopted in which (i) the SN light curve flux measurements in each ...observing filter are fitted separately to an analytical parametrized function that is sufficiently flexible to accommodate virtually all types of 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 evidence for the model, are used as the input feature vector to a classification neural network 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 Classification Challenge (SNPCC), consisting of light curves for 20 895 SNe in total. We consider several random divisions of the data into training and testing sets: for instance, for our sample
(
), a total of 10 (40) per cent of the data are involved in training the algorithm and the remainder used for blind testing of the resulting classifier; we make no selection cuts. Assigning a canonical threshold probability of p
th = 0.5 on the network output to class an SN as Type Ia, for the sample
(
) we obtain a completeness of 0.78 (0.82), purity of 0.77 (0.82) and SNPCC figure of merit of 0.41 (0.50). Including the SN host-galaxy redshift and its uncertainty as additional inputs to the classification network results in a modest 5-10 per cent increase 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 calculate the expected completeness, purity and figure of merit (or other measures of classification quality) as a function of the threshold probability p
th, 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 optimizing p
th and can easily be extended to divide non-Ia SNe into their different classes.
Stellar radial velocity (RV) measurements have proven to be a very successful method for detecting extrasolar planets. Analysing RV data to determine the parameters of the extrasolar planets is a ...significant statistical challenge owing to the presence of multiple planets and various degeneracies between orbital parameters. Determining the number of planets favoured by the observed data is an even more difficult task. Bayesian model selection provides a mathematically rigorous solution to this problem by calculating marginal posterior probabilities of models with different number of planets, but the use of this method in extrasolar planetary searches has been hampered by the computational cost of the evaluating Bayesian evidence. None the less, Bayesian model selection has the potential to improve the interpretation of existing observational data and possibly detect yet undiscovered planets. We present a new and efficient Bayesian method for determining the number of extrasolar planets, as well as for inferring their orbital parameters, without having to calculate directly the Bayesian evidence for models containing a large number of planets. Instead, we work iteratively and at each iteration obtain a conservative lower limit on the odds ratio for the inclusion of an additional planet into the model. We apply this method to simulated data sets containing one and two planets and successfully recover the correct number of planets and reliable constraints on the orbital parameters. We also apply our method to RV measurements of HD 37124, 47 Ursae Majoris and HD 10180. For HD 37124, we confirm that the current data strongly favour a three-planet system. We find strong evidence for the presence of a fourth planet in 47 Ursae Majoris, but its orbital period is suspiciously close to 1 yr, casting doubt on its validity. For HD 10180 we find strong evidence for a six-planet system.
This paper aims to investigate the temporal dynamics within the dorsal anterior cingulate cortex (dACC) and the rostral-ventral (rv) ACC during the interaction of emotional valence and arousal with ...cognitive control in patients with Schizophrenia (SZ). Although cognitive deficits in SZ are highly relevant and emotional disturbances are common, the temporal relationship of brain regions involved in the interaction of emotional and cognitive processing in SZ is yet to be determined. To address this issue, the reaction time (RT), event-related potential (ERP) and temporal dynamics of the dACC and rvACC activity were compared between SZ subjects and healthy controls (HC), using a modified emotional Stroop experiment (with factors namely congruence, arousal and valence). EEG was recorded with 64 channels and source localisation was performed using the sLORETA software package. We observed slower initial increase and lower peaks of time course activity within the dACC and rvACC in the SZ group. In this particular group, the dACC activity during late negativity was negatively correlated with a significantly higher RT in the high arousal conflict condition. In contrast to HC subjects, at the N450 window, there was no significant valence (ERP and rvACC ROI) modulation effect in the SZ subjects. Using high density EEG and source localisation, it was possible to distinguish various disturbances within the dACC and rvACC in patients with SZ, during emotion–cognition processing.
Abstract
A network energy management and optimisation are frequently associated to the network lifetime (maximum operation of nodes in a network) that is contributed by heterogeneous energy ...consumption pattern among nodes arranged in a pipeline layout. This scenario becomes even more critical in a remote monitoring application of an oil and gas pipeline network where a series of sensing points (commonly battery powered wireless nodes) are needed to communicate the measurements to a centralised monitoring station. This paper introduces the Active High Transmitter-receiver energy model (AHiT) which was designed as an adaptive sleep/wake for sensor nodes to optimise energy consumption in the long run. Implementing AHiT energy model on sensor nodes improves the energy consumption based on data transfer activity in a multi-hop pipeline layout wireless sensor network (WSN). In this research, the proposed AHiT energy model optimises node energy by the demand that is unlike to the conventional sleep and wake energy model that is operated on a predefined scheduling scheme that accommodates the data traffic pattern in a network. Generally, in a pipeline network where sensor nodes connectivity is considered critical among neighbouring nodes to support data transfer from one end to the other end of a network. Simulations results in NS2 has indicated node energy consumption is approximately 60% with extended network lifetime around 30% subjected to the data traffic pattern as compared to the conventional energy model.
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