Yeah I didn't compute the Bayes factor mostly because I'm on mobile and was heading out the door. But when the prior you are plugging in is "did this person murder their son", you need a pretty hefty likelihood ratio to push that into the territory of "lock this person up for life".

If you have p(D|H) = 0.8 (hit rate) and p(D|H') = 0.05 (false positive), that gives an LR (likelihood ratio) of 16.

But that's if you had like, a perfect detection situation. I'm not a fan, but it's probably enough to push a search into probable cause°, since if you find contraband, you now have field drug tests, which are also kinda crap°°, but it pushes your hypothesis. Then you seize the drugs and have the highly sensitive and selective lab tests of chemical analysis at your disposal. You have a chain of tests updating your prior.

We have no such chain in the cabin test. It's just "dog signaled" -> some other circumstantial evidence -> jury convicts of murder.

° - that's assuming the handler is being unbiased, vs just giving the cops an excuse to search.

°° - field drug tests basically only catch broad classes of molecules or functional groups, when performed correctly. Like drug dogs, often they too are just theater to intimidate/coerce more searching