Statistical errors and cot death

Very interesting. Of course, it immediately brings up the association with the Roy Meadow case in Britain that I use to illustrate this issue (Munchausen by proxy). But here, it seems, it’s not a statistical error like there. After all, there was evidence from the diaries, four babies is not the same as two (the probability here of an independent accidental death is truly zero, much less than two). There was talk from her (she practiced the version for the court), etc. Therefore, it is possible that probabilistically there was a correct basis for suspicion here. What changed is the new scientific findings, which show that there were medical causes of death, and that changes the picture. It seems to me that, unlike Roy Madow, who also made an error in the actual consideration, the only error here on the statistical level is ignoring the assumption that there could be a connection/dependence between the cases (such as a genetic connection). In other words, these are not independent cases, and therefore the probability of their occurrence is not the product of the probabilities. This error was also made by Madow, but as mentioned, he had other errors (accidental cot death of two children is a possible probability if you test it on all mothers in Britain or the world. Four is definitely not). By the way, she was in prison based on misinterpretation (or lack of scientific information), but even now there is no certainty that she did not murder them. The probability of this becomes such that it is no longer possible to convict (not beyond reasonable doubt). I still do not think that suspicion against her is nullified.