ASAIP Editors' Blog: March 2014
The wider astronomical research community has difficulty in assimilating progress in astrostatistics and astroinformatics because information relevant to a particular problem is often difficult to identify. This problem is pervasive in all fields at the frontiers of methodological research. In this blog, we highlight a few of many potential `gems' buried in the astronomical literature that may have broad applications in different fields. All of these are papers that have appeared in ASAIP Recent Papers listing in January and February 2014.
Digging into the noise for faint source detection
In a recent study nicknamed `Beyond stacking', Ketron Mitchell-Wynne and colleagues (Observatório Astronómico de Lisboa PT) apply a maximum likelihood approach to model source counts below the individual source detection limits in radio images of the sky. They achieve increases up to 10-fold in sensitivity if the location of possible sources is known in advance from prior multiwavelength surveys. Likelihoods are calculated in a 4-parameter space using a Parallel Tempering Markov chain Monte Carlo algorithm. The method is applied to radio interferometry images with very non-Gaussian noise. Similar problems arise in faint source detection at all wavebands.
Progress in unsupervised clustering
Astronomers often obtain multivariate datasets with spatial clustering or heterogeneous classes of an unknown nature. Multi-scale hierarchical clustering procedures (such as the `friends-of-friends' single-linkage algorithm) are commonly used, but they have weak mathematical foundations and reasonable changes in procedure often considerably change outcomes. Brian Kent and colleagues (Carnegie Mellon University USA) implement a longstanding approach from statistician John Hartigan that locates hierarchical regions with high densities. Recent mathematics have shown that Hartigan's `level set tree' dendrogram has strong theoretical properties. Several implementations are available in the R software environment (CRAN packages denpro, gslclust and pdfCluster), but Kent et al. produce a more capable package in Python called DeBaCl (Density-Based Clustering) that treats larger datasets with improved computational efficiency and outcome visualizations.
Comparing Bayesian computational algorithms
Astronomers increasingly investigate the structure of posterior likelihood distributions for large datasets for high-dimensional models. Numerous computational strategies can be considered (see for example theHandbook of Markov Chain Monte Carlo by Brooks et al. 2011). In a recent paper comparing sampling techniques for Bayesian parameter estimation, Rupert Allison and Joanna Dunkley (Univ Oxford UK) examine the performance of Metropolis-Hasting, nested and affine-invariant ensemble MCMC sampling. They find that nested (e.g. the MultiNest algorithm) and affine samplers have lower computational cost with good convergence and scope for parallelization, even for complicated non-Gaussian and multi-modal posteriors.
Blind source separation
Blind source separations seek to separate interesting patterns in astronomical signals from uninteresting signals and noise. These methods can be used for problems ranging from separating cosmological fluctuations from foreground components in the CMB to distinguishing planetary transits from autocorrelated stellar activity. Jeremy Rapin and colleagues (CEA-Saclay FR) are astrophysicsists authoring a paper in the journal IEEE Signal Processing on blind source separation where techniques of `sparsity' are used to enhance contrast between non-negative signals and noise. With their non-negative Generalized Morphological Component Analysis algorithm, separable sources with different morphologies show different coefficients in a sparse representation. Ingo Waldmann (University College Longon UK) develops a related method called ACICA that gives a calibrated Independent Component Analysis using a sparse wavelet representation. It helps with robust detrending of low signal-to=-noise data.
Markus Aschwanden (Lockheed Martin USA) discusses a wide range of astrophysical populations that may be represented as systems with self-organized criticality. SOC systems are scale-free fractal populations with powerlaw size distributions arising from nonlinear conditions that are driven towards a critical intability threshold. SOC size distributions are fitted to populations of lunar craters, asteroids, solar flares, soft gamma ray repeaters, cosmic rays, and other astrophysical systems.