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The variational Bayes method for inverse regression problems with an application to the palaeoclimate reconstruction

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Figure

Figure 1: Proportions of each of the 14 different categorizations against radiocarbon years BP (verticalaxis) at Glendalough (Haslett et al., 2006).
Figure 2: Histogram of the count data on the taxon (left) Alnus and (right) Corylus.
Figure 3: (Left) the black line denotes the true value of the response for the taxon, blue line is for theestimated response, red lines show the 95% HPD region, the blue asterisks represent the observations ontaxon, the green asterisk stands for the data point on the taxon assumed as a single observation on the fossilpollen, (right) the VB marginal of the ancient climate given the observation on fossil pollen, the red asteriskshows the true (assumed) value of the ancient climate, the first block of the figures are for the Gaussianlikelihood, second block, for the Poisson and the third is for the Zero-Inflated Poisson likelihood.
Figure 4: (Left) the black line denotes the true value of the response for the first taxon, blue line is forthe estimated response, red lines show the 95% HPD region, the blue asterisks represent the observationson taxon, the green asterisk stands for the data point on the taxon assumed as a single observation on thefossil pollen, (right) the VB marginal of the ancient climate given the observation on fossil pollen, the redasterisk shows the true (assumed) value of the ancient climate.

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