In my case, the robins built in a honeysuckle bush (a large honeysuckle bush....) in front of the kitchen window. I did not see a Jay in the bush, but the robins did send them packing when they showed up elsewhere in the garden.
My prime candidates are aerial rats, I am sad to say.
"Halton Hills" ' post and picture is an option, but squirrels climb walls.
I suppose the whole thing comes down to how many rats, jays and cowbirds are in your specific area...