The mirror test is interesting for sure, especially in a cross-species context. However, I'm far from convinced about the straightforward reading of "the expected response indicates the subject has an internal map of oneself." Since you read the Wikipedia article down that far, you could also scroll down to the "Criticisms" section and see a variety of objections to that.
Moreover, when asked to choose between the interpretation that the test isn't sufficient for its stated purpose, and the interpretation that six-year olds in Fiji aren't self-aware I rather suspect the former is more likely.
Besides all that, even if we assume self-awareness is the thing you seem to be making of it, I'm not clear how that would draw moral-worth line so neatly between humans (or some humans) and literally everything else. From a consequentialist perspective, if I assume that dogs or rats can experience pain and suffering, it seems weird to neglect them from my utility function on the basis they don't jump through that particular (ambiguous, methodologically-questionable) experimental hoop.
Oh, I agree that the mirror test is quite imperfect. The practical issue is how to draw a Schelling somewhere sensible. Clearly mosquitoes can be treated as non-sentient, clearly most humans cannot be. Treating human fetuses and some mammals as non-sentient is rather controversial. Just "experiencing pain" is probably too wide a net for moral worth, as nociceptors are present in most animals, including the aforementioned mosquito. Suffering is probably a more restrictive term, but I am not aware of a measurable definition of it. It is also probab...
Why is Bayes' Rule useful? Most explanations of Bayes explain the how of Bayes: they take a well-posed mathematical problem and convert given numbers to desired numbers. While Bayes is useful for calculating hard-to-estimate numbers from easy-to-estimate numbers, the quantitative use of Bayes requires the qualitative use of Bayes, which is noticing that such a problem exists. When you have a hard-to-estimate number that you could figure out from easy-to-estimate numbers, then you want to use Bayes. This mental process of testing beliefs and searching for easy experiments is the heart of practical Bayesian thinking. As an example, let us examine 1 Kings 3:16-28:
Notice that Solomon explicitly identified competing hypotheses, raising them to the level of conscious attention. When each hypothesis has a personal advocate, this is easy, but it is no less important when considering other uncertainties. Often, a problem looks clearer when you branch an uncertain variable on its possible values, even if it is as simple as saying "This is either true or not true."
Solomon considers the empirical consequences of the competing hypotheses, searching for a test which will favor one hypothesis over another. When considering one hypothesis alone, it is easy to find tests which are likely if that hypothesis is true. The true mother is likely to say the child is hers; the true mother is likely to be passionate about the issue. But that's not enough; we need to also estimate how likely those results are if the hypothesis is false. The false mother is equally likely to say the child is hers, and could generate equal passion. We need a test whose results significantly depend on which hypothesis is actually true.
Witnesses or DNA tests would be more likely to support the true mother than the false mother, but they aren't available. Solomon realizes that the claimant's motivations are different, and thus putting the child in danger may cause the true mother and false mother to act differently. The test works, generates a large likelihood ratio, and now his posterior firmly favors the first claimant as the true mother.