Confusion about PoE fusion

[microcourier]

Thanks for your great paper. I have a confusion about the PoE part and wonder if you can clarify it.

In the paper, Definition 1 shows that the posterior is made by PoE, but i don't realize how we did it.

I tried to find the answer in the code, and came down to poe
It seems to be adding mus and vars but not product it,what is the meaning of it?

I would apologize if it's a naive question, since i just study ML for a short time,and i will appreciate it if you could clarify it.
Thank a lot.

[thomassutter]

Hi, you are looking at the correct location.
The referenced function follows the computation of the PoE for Gaussian distribution, which is possible in closed form.
Maybe also look here:
product of two gaussian pdfs