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statistics. Yet the way it's formulated here, one would think it is fundamentally connected to the notion of priors, likelihoods and posteriors, and that it involves "evidence," data and hypotheses. These are terms used by the modern bayesian and are much later ideas. I wish Bayes's Rule were not introduced as if it were bound up with the more modern notions of evidence, priors and posteriors, and as if, to employ it, you had to think the way modern bayesians think. If someone reading this has a feeling of ownership on this section, I urge you to introduce the rule as it is (a relation between joint and conditional probabilities) without the modern bayesian terminological overhead. Bayesians and non-bayesians alike use Bayes Rule.
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formula for performing updates. The quote by
Hacking which is a large fraction of the subsection's text is more philosophical than mathematical and in any case uses many terms in a technical way without defining them or linking to any standard definitions. It seems to me the section needs to either be cut or expanded. I was initially interested in the subsection because as a non-expert I was wondering if anybody actually uses alternative rules in practice. Perhaps the answer is "no" and such things are relegated to philosophy journals?
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I can get nothing out of the subsection "Alternatives to
Bayesian updating" as currently written. I am a working mathematician, though not in probability or statistics, and I do not believe the problem is mine. The subsection is extremely vague and does not for instance include any alternative
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The term 'likelihood' has a long tradition in both frequentist and
Bayesian statistics, and there are technical reasons why it is not called a probability. The application of Bayes' rule becomes trickier when you add statistical parameters into the mix, which is why the statistical terminology
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The statement of Bayes's rule bothers me. Bayes's Rule is a mathematical description of the relation between joint probability and conditional probability. Every statistician, whether "frequentist" or bayesian, uses Bayes. It's an indispensable mathematical fact of elementary probability and
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For the 'Examples', I think it would be useful to contrast this approach with a frequentist approach. This would be especially interesting if the frequentist approach used a different formula, yielded a different result, or was not calculable. Conversely, for the current 'Probability of a
406:"The likelihood function is a function of the evidence, E {\displaystyle \textstyle E} \textstyle E, while the posterior probability is a function of the hypothesis, H {\displaystyle \textstyle H} \textstyle H." I think technically both are functions of both H and E. --
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Is that meant to address my point? Not sure who you're responding to, but I see no relation between my point and your response. I did not mention the likelihood at all. I'm quite familiar with what a likelihood is and why it's called what it's called.
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updating is. I guess that it involves modifying the prior probability in the light of the new evidence, but whether this is done simply by substituting the 'posterior' probability, or something more complicated, is not clear.
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This section uses archaeology as an example in a way that bears no relation to how archaeology would deal with the hypothetical scenario and isn't clear.
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diverges from elementary probability. The section could do with providing more motivation for the definitions. —
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