32 research outputs found

    Models and algorithms for image reconstruction

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    Improving power posterior estimation of statistical evidence

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    The statistical evidence (or marginal likelihood) is a key quantity in Bayesian statistics, allowing one to assess the probability of the data given the model under investigation. This paper focuses on refining the power posterior approach to improve estimation of the evidence. The power posterior method involves transitioning from the prior to the posterior by powering the likelihood by an inverse temperature. In common with other tempering algorithms, the power posterior involves some degree of tuning. The main contributions of this article are twofold -- we present a result from the numerical analysis literature which can reduce the bias in the estimate of the evidence by addressing the error arising from numerically integrating across the inverse temperatures. We also tackle the selection of the inverse temperature ladder, applying this approach additionally to the Stepping Stone sampler estimation of evidence.Comment: Revised version (to appear in Statistics and Computing). This version corrects the typo in Equation (17), with thanks to Sabine Hug for pointing this ou

    Tuning tempered transitions

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    Bayesian Object Identification

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    This paper addresses the task of locating and identifying an unknown number of objects of different types in an image. Baddeley & Van Lieshout (1993) advocate marked point processes as object priors, whereas Grenander & Miller (1994) use deformable template models. In this paper elements of both approaches are combined to handle scenes containing variable numbers of objects of different types, using reversible jump Markov chain Monte Carlo methods for inference (Green, 1995). The naive application of these methods here leads to slow mixing and we adapt the model and algorithm in tandem in proposing three strategies to deal with this. The first two expand the model space by introducing an additional `unknown' object type and the idea of a variable resolution template. The third strategy, utilising the first two, augments the algorithm with classes of updates which provide intuitive transitions between realisations containing different numbers of cells by splitting or merging nearby objects. Some key words: Bayesian inference; Deformable template; Image analysis; Marked point process; Markov chain Monte Carlo; Object recognition; Variable dimension distribution. 1 INTRODUCTION Statistical approaches to image analysis are often divided into `low-level' and `high-level' methods. The former category generally involve pixel-level Markov random field models. High-level tasks such as object recognition require models and algorithms which deal with the components of the image on a global scale. Two main approaches have emerged in the Bayesian approach to high--level imaging. The first is based on pattern theory (Grenander, 1993). The theory gives an algebraic framework, image algebras, for describing patterns as structures regulated by various rules; natural variability is rep..