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Abstract BSiZer is a smoothing‐based Bayesian data analysis tool that can be used to find scale‐dependent features in scatter plots. It uses a scale space approach which means that, instead of just one smooth, a whole family of smoothing levels are explored, with each level thought to describe the object of interest at a particular scale or resolution. While the original BSiZer was used to analyze curves underlying noisy data, we discuss also its subsequent extensions to the analysis of images and random fields. The methodology is demonstrated with applications to climate reconstruction and prediction and image analysis. © 2010 John Wiley & Sons, Inc. This article is categorized under: Statistical Learning and Exploratory Methods of the Data Sciences > Knowledge Discovery

An example of BSiZer analysis. Upper panel: the true underlying curve (in red) y = t + 17sin(t) + 20sin(0.5t), observations (dots) on the grid 1,2,…,75 obtained by adding N(0,102)‐noise to the true values and a family of smooths (in blue) obtained as posterior means. Lower panel: the credibility map based on the posterior probability threshold α = 0.8.

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Scale space multiresolution analysis of global winter temperature change (in °C) from 1980–2000 to 2080–2100 as predicted by the consensus of 21 climate prediction models. For more details, see the text.

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The iBSiZer atlas for an artificial test example. First row: the true difference image and posterior means of its smooths with a yellow circle indicating the effective range of the smoother. Second row: the noisy observed image and four credibility maps.

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Six top panels: Holocene temperature reconstructions based three proxy records (chironomids, diatoms, and pollen) from two lakes in northern Fennoscandia (Lake Toskal and Lake Tsuolbmajavri). Bottom panel: BSiZer credibility analysis of consensus temperature anomaly features supported by these reconstructions.

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BSiZer analysis of a diatom fossil based temperature reconstruction in northern Fennoscandia for the last 800 years. The upper panel: the reconstructed temperatures shown as dots together with three smooths obtained as posterior means. The lower panel: BSiZer map with the three smoothing levels shown using the same colors as in the upper panel.

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Statistical Learning and Exploratory Methods of the Data Sciences > Knowledge Discovery

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