Using the MLE to select the prior distribution…empirical Bayes?

It was requested that I read the following article for work: https://support.sas.com/resources/papers/proceedings15/1400-2015.pdf

In Case II, the author starts by doing two things:

First, he computes the maximum likelihood estimator for the PD parameter $$\lambda$$, denoted $$\hat \lambda$$. Second, he chooses the prior $$p(\lambda)$$ so that $$E_{\lambda}[\lambda]=\hat\lambda$$.

I am not an expert with Bayesian inference, but my understanding tells me that this is totally contrary to the philosophy of Bayesian inference. We are working with a very small data set, and so there is very little information contained in the data. By using the data to construct the prior, we are essentially building a posterior distribution by incorporating the information in the data with itself. I understand that there is a method called "empirical bayes", but from what I understand, this involves computing the MLE from the marginal distribution of the data $$x$$, not from the conditional distribution $$p(x|\lambda)$$. In other words, if we have subgroups within the data, I understand Empirical Bayes to be when we use data from all subgroups to build a prior regarding a particular subgroup. In the above article I cited, only the data from a particular subgroup is used to build the prior for that subgroup.

Can someone tell me if this is common practice in Bayesian stats? I have never seen anyone do this, and I would like to sound more informed if I tell my boss that the methodology is flawed.

• This is very low-key empirical Bayes indeed. – Xi'an Sep 10 '20 at 18:31