Perhaps a better example of how a naive assumption of statistical independence has led to a severe miscarriage of justice is provided by the case of Sally Clark

Perhaps a better example of how a naive assumption of statistical independence has led to a severe miscarriage of justice is provided by the case of Sally Clark: https://en.wikipedia.org/wiki/Sally_Clark https://en.wikipedia.org/wiki/Sally_Clark I would be extremely wary of your claim that "multiple accusations enable us to get enough evidence to convict even in parameter regimes where a single accusation is never enough" (https://www.dropbox.com/sh/drrvcd5zzqclhbt/AACdWnx_wlfwnUoYFme9UgX9a/exercises_with_binomial_posterior_probabilities.pdf?dl=0 https://www.dropbox.com/sh/drrvcd5zzqclhbt/AACdWnx_wlfwnUoYF...).