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ABSTRACT: The Sloan digital sky survey is an extremely large astronomical survey that is conducted with the intention of mapping more than a quarter of the sky. Among the data that it is generating are spectroscopic and photometric measurements, both containing information about the red shift of galaxies. The former are precise and easy to interpret but expensive to gather; the latter are far cheaper but correspondingly more difficult to interpret. Recently, Csabai and co-workers have described various calibration techniques aiming to predict red shift from photometric measurements. We investigate what a structured Bayesian approach to the problem can add. In particular, we are interested in providing uncertainty bounds that are associated with the underlying red shifts and the classifications of the galaxies. We find that quite a generic statistical modelling approach, using for the most part standard model ingredients, can compete with much more specific custom-made and highly tuned techniques that are already available in the astronomical literature. Copyright (c) 2008 Royal Statistical Society.
Journal of the Royal Statistical Society Series C. 01/2008; 57(4):487-504.
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ABSTRACT: Images are the source of information in many areas of scientific enquiry. A common objective in these applications is the reconstruction of the true scene from a degraded image. When objects in the image can be described parametrically, reconstruction can proceed by fitting a high level image model. We consider the analysis of "confocal fluorescence microscope" images of cells in an area of cartilage growth. Biological questions that are posed by the experimenters concern the nature of the cells in the image and changes in their properties with time. Our model of the imaging process is based on a detailed analysis of the data. We treat the true scene as a realization of a "marked point process", incorporating this as the "high level" prior model in a Bayesian analysis. Inference is by simulation using "reversible jump" versions of "Markov chain Monte Carlo" algorithms which can handle the varying dimension of the image description arising from an unknown number of cells, each with its own parameters. Copyright 2004 Royal Statistical Society.
Journal of the Royal Statistical Society Series C. 01/2004; 53(1):31-49.
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ABSTRACT: Recent articles have commented on the difficulty of proposing efficient reversible jump moves within MCMC. We suggest a new way to make proposals more acceptable using a secondary Markov chain to modify proposed moves—at little extra programming cost.
Statistics & Probability Letters.
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ABSTRACT: We report methods for tackling a challenging three-dimensional (3D) deconvolution problem arising in confocal microscopy. We fit a marked point process model for the set of cells in the sample using Bayesian methods; this produces automatic or semi-automatic segmentations showing the shape, size, orientation and spatial arrangement of objects in a sample. Importantly, the methods also provide measures of uncertainty about size and shape attributes. The 3D problem is considerably more demanding computationally than the two-dimensional analogue considered in Al-Awadhi et al. [2] due to the much larger data set and higher-dimensional descriptors for objects in the image. In using Markov chain Monte Carlo simulation to draw samples from the posterior distribution, substantial computing effort can be consumed simply in reaching the main area of support of the posterior distribution. For more effective use of computation time, we use morphological techniques to help construct an initial typical image under the posterior distribution.
Journal of Applied Statistics. 38(1):29-46.
