I used "ontology" here to mean the definitions in your model. E.g. boojums, snarks and monsters in the examples above. If you wanted to update your model itself based on observations and remain within the Bayesian framework, you'd have to have had the foresight to anticipate doing so, and provided a collection of different models with a prior over them.
You are right. Thank you for the correction, and I like your description which I hope you don't mind me using (with credit) when I edit this post. My error was not realizing that P(boojum(x)|snark(x)) is the marginal probability for one particular row in the table. Even though the syntax is (hopefully) valid, this stuff is still confusing to think about!
and he similarly thinks about the dummy variable of the quantifier that way, and so how could all these different cats have the same propability?
I'm not quite sure how Chapman is interpreting these thin...
The arguments for Bayesian epistemology embodying rationality. It would be helpful to see this position elucidated all in one place.
tristanm writes "I’ve noticed a recent trend towards skepticism of Bayesian principles and philosophy ... which I have regarded with both surprise and a little bit of dismay, because I think progress within a community tends to be indicated by moving forward to new subjects and problems rather than a return to old ones that have already been extensively argued for and discussed." These extensive arguments and discussions abou...
I'm being too vague with my use of the word "model". By "model" I just mean some set of possibilities that are grouped together. For instance in machine learning, a model is a parametrized function (which can be regarded as a set of functions each indexed by a parameter). A set of different models is also a model (just more possibilities). Maybe this is not the best word to use.
In the case of Solomonoff induction, some of those programs might contain logic that appear to simulate simple environments with 3D space containing stuff, such as chairs and cars, ... (read more)