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My current understanding is that logistic regression can be used for 2 tasks:

1) Binary Classification 2) Computing a probability between 0 and 1 for data generated by a Bernoulli process?

I also know there's more than one way to solve a logistic regression problem, one being the bayesian way, one being MLE and the other having to do with general linear models and link functions.

In what circumstances is bayesian logistic regression preferred?

MrL
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    Simplistically it would be whenever there is strong prior. This would be true for any statistical problem where Bayesian methods can be used. – Michael R. Chernick Mar 26 '18 at 20:48

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