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Visualization in Bayesian data analysis. (English) Zbl 1140.68519

Chen, Chun-houh (ed.) et al., Handbook of data visualization. Berlin: Springer (ISBN 978-3-540-33036-3/hbk). Springer Handbooks of Computational Statistics, 709-724 (2008).
Summary: Exploratory data analysis and modeling can work well together: in our applied research, graphs are used to comprehend and check models. In the initial phase, we create plots that show us how the models work, and then plot data and compare it to the model to see where more work is needed.
We gain insight into the shortcomings of the model by performing graphical model checks. Graphs are most often drawn in order to compare data with an implicit reference distribution (e.g. Poisson model for rootograms, independence-with-mean-zero for residual plots, or normality for quantile-quantile plots), but we would also include more general comparisons; for example, a time series plot is implicitly compared to a constant line. In Bayesian data analysis, the reference distribution can be formally obtained by computing the replication distribution of the observables; the observed quantities can be plotted against draws from the replication distribution to compare the fit of the model.
We aim to make graphical displays an integrated and automatic part of data analysis. Standardized graphical tests must be developed, and these should be routinely generated by the modeling and model-fitting environment.
For the entire collection see [Zbl 1187.68001].

MSC:

68U10 Computing methodologies for image processing
62-07 Data analysis (statistics) (MSC2010)
62A09 Graphical methods in statistics

Software:

R; R2WinBUGS
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