Concept of inverse probability

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I'm a student of statistic and recently I start learning about inference statistic.

In some papers the authors cite the inverse probability, but for me the concept is like bayesian statistic. Which is the difference between the inverse probability and bayesian statistic? Which is the true concept of inverse probaility? Thanks!

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They are the same thing. As the wikipedia article makes clear, the term "Bayesian" did not come into common use until the 1950's, even though the idea is 200 years older.