File:part1-fig-06-fruit-posterior.png

Figure file · Bayesian hypotheses and model comparison

The fruit posterior \operatorname{Gamma}(189,21), with the region \theta\leq10 shaded. The two summaries disagree in appearance only. The equal-tailed interval must leave 2.5\% in each tail, so its upper endpoint is pushed past 10; the shaded area answers a different question and puts 93.3\% of the mass at or below the boundary. Reading the crossing as a rejection substitutes one summary for the other.

The fruit posterior \operatorname{Gamma}(189,21), with the region \theta\leq10 shaded. The two summaries disagree in appearance only. The equal-tailed interval must leave 2.5\% in each tail, so its upper endpoint is pushed past 10; the shaded area answers a different question and puts 93.3\% of the mass at or below the boundary. Reading the crossing as a rejection substitutes one summary for the other.

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Summary

Description. The fruit posterior \operatorname{Gamma}(189,21), with the region \theta\leq10 shaded. The two summaries disagree in appearance only. The equal-tailed interval must leave 2.5\% in each tail, so its upper endpoint is pushed past 10; the shaded area answers a different question and puts 93.3\% of the mass at or below the boundary. Reading the crossing as a rejection substitutes one summary for the other.

Appears in. Bayesian hypotheses and model comparison

Made by. A figure from the course chapter.

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