If you consider subjective priors to be a problem, this can be addresses to
some degree using so called &quot;objective priors&quot;. They are objective in a sense
that if two people agree on underlying principles of how priors should be
assigned, then they will get the same priors. Catch is that you must decide
what principles to use, as they are not objective themselves.<p>Updating multiple times on the same evidence can be bad - as it overstates
evidence you have for some hypothesis - but you could do much worse. Instead of
discovering that H implies E, suppose instead that you conditioned on H, which
as later turned out is logically inconsistent. This is in general serious
mistake regardless if what you are doing have word &quot;frequentist&quot; or &quot;Bayes&quot;
attached to it, but consequences are not necessarily always the same. Larry
Wasserman in chapter titled &quot;Strengths and Weaknesses of Bayesian Inference&quot; of
his &quot;All of Statistics&quot; have an example concerned with estimating a normalizing
constant. He compares the two approaches, frequentist one which works just
fine, and Bayes one which fails miserably. There is no additional commentary so
I always wondered if he never realized that derivation makes inconsistent
assumptions, or he realized that but intended to show that frequentist comes
out just fine. Ex falso quod libet.<p>Regarding the raven paradox, the underlying reasoning and conclusions always
appeared to me to perfectly natural and reasonable. I think it is to great
detriment for mathematics and statistics, that people come up with catch names
with word &quot;paradox&quot; in it, for things that are merely unintuitive to them. For
example Simpson&#x27;s paradox is a simple observation that: probability of an
event, is not a simple average of event probability across all groups, instead
those within group event probabilities should be also weighted by relative
group sizes. Whats paradoxical about that?<p>Regarding negation of H, not being a real hypothesis -- this is only true if
you claim that you somehow consider all alternative hypotheses. I don&#x27;t think
people claim that. I seems to me that it is rather taken to represent only
those alternative hypothesis that are under consideration given your modeling
assumptions. Then it is perfectly fine and valid. I like how Jaynes avoided this
kind of misinterpretations by conditioning everything on background information
used and other assumptions. Let all of those be represented by B. Then you
would talk about P(H|B) and P(~H|B), which makes it clearer that you don&#x27;t
talk all unknown unknowns.