13 hours ago
- Traditional Bayesian reasoning requires setting a prior before seeing data, but in complex real-world problems, the space of possibilities is vast and often unknown until after data is observed.
- Basing a prior solely on pre-data assumptions can lead to misleading conclusions, as shown in the alien example where a coarse prior yields a 50% posterior probability, while a finer categorization gives a 10% posterior.
- The core issue is that practical Bayesian analysis relies on discretizing an infinite possibility space, and the quality of the approximation depends on choosing categories that align with the data's likelihood.
- A practical solution is to first examine the data to identify important categories, then retroactively assess how plausible those categories would have been before seeing the data.