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Classifying X-ray Binaries: A Probabilistic Approach
Aug 17, 2018
In X-ray binary star systems consisting of a compact object that accretes material from an orbiting secondary star, there is no straightforward means to decide if the compact object is a black hole or a neutron star. To assist this classification, we develop a Bayesian statistical model that makes use of the fact that X-ray binary systems appear to cluster based on their compact object type when viewed from a 3-dimensional coordinate system derived from X-ray spectral data. The first coordinate of this data is the ratio of counts in mid to low energy band (color 1), the second coordinate is the ratio of counts in high to low energy band (color 2), and the third coordinate is the sum of counts in all three bands. We use this model to estimate the probabilities that an X-ray binary system contains a black hole, non-pulsing neutron star, or pulsing neutron star. In particular, we utilize a latent variable model in which the latent variables follow a Gaussian process prior distribution, and hence we are able to induce the spatial correlation we believe exists between systems of the same type. The utility of this approach is evidenced by the accurate prediction of system types using Rossi X-ray Timing Explorer All Sky Monitor data, but it is not flawless. In particular, non-pulsing neutron systems containing "bursters" that are close to the boundary demarcating systems containing black holes tend to be classified as black hole systems. As a byproduct of our analyses, we provide the astronomer with public R code that can be used to predict the compact object type of X-ray binaries given training data.
* Editing of figure captions and correction of y-axis labels for bar charts in figures 6 and 7
Admissibility of a posterior predictive decision rule
Sep 09, 2017Recent decades have seen an interest in prediction problems for which Bayesian methodology has been used ubiquitously. Sampling from or approximating the posterior predictive distribution in a Bayesian model allows one to make inferential statements about potentially observable random quantities given observed data. The purpose of this note is to use statistical decision theory as a basis to justify the use of a posterior predictive distribution for making a point prediction.
Quantification of observed prior and likelihood information in parametric Bayesian modeling
Sep 07, 2017
Two data-dependent information metrics are developed to quantify the information of the prior and likelihood functions within a parametric Bayesian model, one of which is closely related to the reference priors from Berger, Bernardo, and Sun, and information measure introduced by Lindley. A combination of theoretical, empirical, and computational support provides evidence that these information-theoretic metrics may be useful diagnostic tools when performing a Bayesian analysis.