diff --git a/blog/2023/02/04/just-in-time-bayesianism/index.md b/blog/2023/02/04/just-in-time-bayesianism/index.md index c74af4e..106d3b0 100644 --- a/blog/2023/02/04/just-in-time-bayesianism/index.md +++ b/blog/2023/02/04/just-in-time-bayesianism/index.md @@ -78,9 +78,7 @@ Just-in-time Bayesianism would explain this as follows. \end{cases} \] -The second estimate is the estimate produced by [Laplace's law](https://en.wikipedia.org/wiki/Rule_of_succession)---an instance of Bayesian reasoning given an ignorance prior---given one "success" (a dog biting a human) and \(n\) "failures" (a dog not biting a human). - -Now, because the first hypothesis assigns very low probability to what the man has experienced, a whole bunch of the probability goes to the second hypothesis. Note that the prior degree of credence to assign to this second hypothesis *isn't* governed by Bayes' law, and so one can't do a straightforward Bayesian update. +The second estimate is the estimate produced by [Laplace's law](https://en.wikipedia.org/wiki/Rule_of_succession)---an instance of Bayesian reasoning given an ignorance prior---given one "success" (a dog biting a human) and \(n\) "failures" (a dog not biting a human).

Now, because the first hypothesis assigns very low probability to what the man has experienced, a whole bunch of the probability goes to the second hypothesis. Note that the prior degree of credence to assign to this second hypothesis *isn't* governed by Bayes' law, and so one can't do a straightforward Bayesian update.

But now, with more and more encounters, the probability assigned by the second hypothesis, will be as \(\frac{2}{n+2}\), where \(n\) is the number of times the man interacts with a dog. But this goes down very slowly: