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?
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 $Y = 1$.
Answered in comments by Jon:
Try: We are using "counts" only to make the prediction". Unless you're doing Bayesian Logistic regression, don't use the word prior.
