# The usage of word "prior" in logistic regression with intercept only

Suppose I am fitting a logistic regression with intercept only, which is equivalent tho using the count to estimate the outcome probability and make prediction.

Can I say following?

We are using prior only to make the prediction.

I think some persons from CV corrected me, that the word prior has close relationship with Bayesian statistics, and the statement is not correct.

If it is not accurate, what should I say if we only use the counts to estimate the outcome probability?

• Try: We are using "counts" only to make the prediction"
– Jon
Commented Aug 15, 2016 at 18:28
• Unless you're doing Bayesian Logistic regression, don't use the word prior.
– Jon
Commented Aug 15, 2016 at 18:29
• If I read that, it would sound like a tautology. Of course in any Bayesian estimation a prior is used to make the posterior which is the prediction! Just don't use the word prior if it's not Bayesian. Commented Aug 15, 2016 at 18:36

I say it's fine.

Logistic regression estimates $$P(Y = 1\vert X = x)$$.

$$P(Y = 1\vert X = x) = \dfrac{ P(X = x\vert Y = 1)P(Y = 1) }{ P(X = x) }$$

$$P(Y = 1)$$ is the prior probability that $$Y = 1$$.

If we only use an intercept in our model, no matter what features we have, then the probability predicted by the logistic regression model is the proportion of $$Y$$-values with $$Y = 1$$. This is $$P(Y = 1)$$, so the prior probability that $$Y = 1$$.