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As long as I clearly do not know the concepts I would try to be very explicit to make my point:

In the chapter 9: Hypothesis testing of the book "Statistical Thinking for the 21st Century" (https://statsthinking21.github.io/statsthinking21-core-site/hypothesis-testing.html) the Null Hypothesis Statistical testing is presented, and then its alternative, the Bayesian hypothesis testing in the chapter 11 (https://statsthinking21.github.io/statsthinking21-core-site/bayesian-statistics.html#bayesian-hypothesis-testing).

In the book "All of statistics" (Larry Wasserman) the chapter 10: Hypothesis testing and p-values describes other methods such as the Wald Test and the Likelihood Ratio Test.

My question is: If you had to do a conceptual scheme with the next elements: "Hypothesis testing", "Null Hypothesis Statistical testing", "Bayesian hypothesis testing", "Wald test" & "Likelihood Ratio Test" how would they be related/connected?

Thank you in advance for any pontential help!

Gero
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  • I consider Wald and Likelihood Ratio (and Rao) tests to be likelihood based inference insofar as they are asymptotically equivalent. Bayesian estimation is not intrinsically inferential. One needs to specify two priors corresponding to two hypotheses to be compared. – AdamO Dec 15 '21 at 19:18
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    Can you rewrite the question to remove parenthetical statements? And please ask one, clear direct question. There's a lot of errors in your setup and I'm not totally sure what you'd like to know. – AdamO Dec 15 '21 at 19:22
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    It might help if you said why you think Wald and likelihood ratio tests are not hypothesis tests. – Dave Dec 15 '21 at 20:23
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    Your question contains several false premises that will make answers difficult to write and even more difficult for you to understand. Maybe start here: https://stats.stackexchange.com/questions/488398/alternatives-to-the-null-hypothesis-significance-testing-framework – Michael Lew Dec 15 '21 at 20:23

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