Inventing the hypotheses and the model in the first place. Bayesian inference updates probabilities over hypotheses already admitted by a model. If reality requires a structure that the model doesn't assign a prior probability to, such as an omitted variable, mechanism, or failure mode, ordinary Bayesian updating cannot recover it, no matter how much data is observed.
For example:
A forecasting model estimates restaurant demand from years of bookings. Then a major concert is announced next door. A local manager immediately expects a packed evening, while the model predicts an ordinary Tuesday because it has never encountered that situation, and was not prepared for it. To do so would have not been reasonable based on the data available to begin with, after all.
So you can have someone opine about how well some argument is supported through Bayesian inference, and how another isn't, but that's only going to keep them honest in a limited sense. They can still miss the bigger picture by e.g. simply not knowing about it, and not knowing to check for it. If you don't either, they done misled you.
This failure mode is identifiable without having to reason about probability theory as well by the way: https://news.ycombinator.com/item?id=48986444
If you're still unconvinced:
- why would BAND have a concert here? no concerts in this area, ever
- doesn't BAND have ties to this place? no sufficient evidence in the way of that
- BAND lead singer has hung out here once and liked THING, decided to have a concert here for sure one day on a whim
Individually, these have low local attributing info available, so you'd never be able to justify the inference. But not being able to justify the inference didn't make the claims wrong, just unfounded. Those are not the same thing. And so chasing probabilities like this, while maximizes how much your position is defensible, also boxes you in. You'll be reasonable in why you thought what you did, but that won't make you necessarily right, despite the suggestions otherwise.