File:part1-fig-02-prior-sensitivity.png

Figure file · The Beta–Binomial model

The three priors, then the posteriors they produce after 3 heads in 10 tosses and after 30 heads in 100. Both datasets have the same observed proportion 0.3, marked by the dashed vertical line, so moving to the right changes only how much weight the data carry. Ten tosses leave three visibly different posteriors; one hundred leave three that have nearly closed on each other and on x/n. Disagreement about the prior is a disagreement about small samples. The \operatorname{Beta}(0.6,0.6) prior is unbounded at 0 and 1, so its curve leaves the top of the first panel.

The three priors, then the posteriors they produce after 3 heads in 10 tosses and after 30 heads in 100. Both datasets have the same observed proportion 0.3, marked by the dashed vertical line, so moving to the right changes only how much weight the data carry. Ten tosses leave three visibly different posteriors; one hundred leave three that have nearly closed on each other and on x/n. Disagreement about the prior is a disagreement about small samples. The \operatorname{Beta}(0.6,0.6) prior is unbounded at 0 and 1, so its curve leaves the top of the first panel.

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Summary

Description. The three priors, then the posteriors they produce after 3 heads in 10 tosses and after 30 heads in 100. Both datasets have the same observed proportion 0.3, marked by the dashed vertical line, so moving to the right changes only how much weight the data carry. Ten tosses leave three visibly different posteriors; one hundred leave three that have nearly closed on each other and on x/n. Disagreement about the prior is a disagreement about small samples. The \operatorname{Beta}(0.6,0.6) prior is unbounded at 0 and 1, so its curve leaves the top of the first panel.

Appears in. The Beta–Binomial model

Made by. A figure from the course chapter.

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