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Register a new userBaTMAn: Bayesian Technique for Multi-image Analysis
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This paper describes the Bayesian Technique for Multi-image Analysis (BaTMAn), a novel image-segmentation technique based on Bayesian statistics that characterizes any astronomical dataset containing spatial information and performs a tessellation based on the measurements and errors provided as input. The algorithm iteratively merges spatial elements as long as they are statistically consistent with carrying the same information (i.e. identical signal within the errors). We illustrate its operation and performance with a set of test cases including both synthetic and real Integral-Field Spectroscopic data. The output segmentations adapt to the underlying spatial structure, regardless of its morphology and/or the statistical properties of the noise. The quality of the recovered signal represents an improvement with respect to the input, especially in regions with low signal-to-noise ratio. However, the algorithm may be sensitive to small-scale random fluctuations, and its performance in presence of spatial gradients is limited. Due to these effects, errors may be underestimated by as much as a factor of two. Our analysis reveals that the algorithm prioritizes conservation of all the statistically-significant information over noise reduction, and that the precise choice of the input data has a crucial impact on the results. Hence, the philosophy of BaTMAn is not to be used as a `black box to improve the signal-to-noise ratio, but as a new approach to characterize spatially-resolved data prior to its analysis. The source code is publicly available at http://astro.ft.uam.es/SELGIFS/BaTMAn .
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The duty cycle (DC) of astrophysical sources is generally defined as the fraction of time during which the sources are active. However, DCs are generally not provided with statistical uncertainties, since the standard approach is to perform Monte Carlo bootstrap simulations to evaluate them, which can be quite time consuming for a large sample of sources. As an alternative, considerably less time-consuming approach, we derived the theoretical expectation value for the DC and its error for sources whose state is one of two possible, mutually exclusive states, inactive (off) or flaring (on), as based on a finite set of independent observational data points. Following a Bayesian approach, we derived the analytical expression for the posterior, the conjugated distribution adopted as prior, and the expectation value and variance. We applied our method to the specific case of the inactivity duty cycle (IDC) for supergiant fast X-ray transients. We also studied IDC as a function of the number of observations in the sample. Finally, we compare the results with the theoretical expectations. We found excellent agreement with our findings based on the standard bootstrap method. Our Bayesian treatment can be applied to all sets of independent observations of two-state sources, such as active galactic nuclei, X-ray binaries, etc. In addition to being far less time consuming than bootstrap methods, the additional strength of this approach becomes obvious when considering a well-populated class of sources ($N_{rm src} geq 50$) for which the prior can be fully characterized by fitting the distribution of the observed DCs for all sources in the class, so that, through the prior, one can further constrain the DC of a new source by exploiting the information acquired on the DC distribution derived from the other sources. [Abridged]
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 parameterises the power at individual frequencies in the signal. We use TempoNest to show that at noise levels representative of current datasets in the European Pulsar Timing Array (EPTA) and International Pulsar Timing Array (IPTA) 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.
Context. The analysis of luminosity and mass distributions of young stellar clusters is essential to understanding the star-formation process. However, the gas and dust left over by this process extinct the light of the newborn stars and can severely bias both the census of cluster members and its luminosity distribution. Aims. We aim to develop a Bayesian methodology to infer, with minimal biases due to photometric extinction, the candidate members and magnitude distributions of embedded young stellar clusters. Methods. We improve a previously published methodology and extend its application to embedded stellar clusters. We validate the method using synthetically extincted data sets of the Pleiades cluster with varying degrees of extinction. Results. Our methodology can recover members from data sets extincted up to Av ~ 6 mag with accuracies, true positive, and contamination rates that are better than 99%, 80%, and 9%, respectively. Missing values hamper our methodology by introducing contaminants and artifacts into the magnitude distributions. Nonetheless, these artifacts vanish through the use of informative priors in the distribution of the proper motions. Conclusions. The methodology presented here recovers, with minimal biases, the members and distributions of embedded stellar clusters from data sets with a high percentage of sources with missing values (>96%).
We describe the method used to detect sources for the Herschel-ATLAS survey. The method is to filter the individual bands using a matched filter, based on the point-spread function (PSF) and confusion noise, and then form the inverse variance weighted sum of the individual bands, including weights determined by a chosen spectral energy distribution. Peaks in this combined image are used to estimate the source positions. The fluxes for each source are estimated from the filtered single-band images, interpolated to the exact sub-pixel position. We test the method by creating simulated maps in three bands with PSFs, pixel sizes and Gaussian instrumental noise that match the 250, 350 and 500 micron bands of Herschel-ATLAS. We use our method to detect sources and compare the measured positions and fluxes to the input sources. The multi-band approach allows reliable source detection a factor 1.2 to 3 lower in flux compared to single-band source detection, depending on the source colours. The false detection rate is reduced by a factor between 4 and 10, and the variance of the source position errors is reduced by about a factor 1.5. We also consider the effect of confusion noise and find that the appropriate matched filter gives a further improvement in completeness and noise over the standard PSF filter approach. Overall the two modifications give a factor of 1.5 to 3 improvement in the depth of the recovered catalogues compared to a single-band PSF filter approach.
The extremely regular, periodic radio emission from millisecond pulsars makes them useful tools for studying neutron star astrophysics, general relativity, and low-frequency gravitational waves. These studies require that the observed pulse times of arrival be fit to complex timing models that describe numerous effects such as the astrometry of the source, the evolution of the pulsars spin, the presence of a binary companion, and the propagation of the pulses through the interstellar medium. In this paper, we discuss the benefits of using Bayesian inference to obtain pulsar timing solutions. These benefits include the validation of linearized least-squares model fits when they are correct, and the proper characterization of parameter uncertainties when they are not; the incorporation of prior parameter information and of models of correlated noise; and the Bayesian comparison of alternative timing models. We describe our computational setup, which combines the timing models of Tempo2 with the nested-sampling integrator MultiNest. We compare the timing solutions generated using Bayesian inference and linearized least-squares for three pulsars: B1953+29, J2317+1439, and J1640+2224, which demonstrate a variety of the benefits that we posit.
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