I struggle with the barking issue, too. Although Bo is the product of a BYB, I know that her father was a working dog on a sheep ranch, so her guarding instincts are pretty strong compared to her mom, who was a non-working Pyr. For the first two years of her life, Bo lived on a 27 acre ranch with two other (older) Pyrs and her barking was never considered a problem. We bought a house last year in a somewhat rural neighborhood, but the neighbors aren't Pyr friendly. They complained, so we can't leave Bo outside unsupervised. She, too, barks at ANYONE or ANYTHING coming near the house (birds, people, especially other dogs, and diesel trucks-not sure about that one). Pyrs don't really excell at obeience, and usually consier your commands more of a request that they have the option of not doing! In our case, we have trained Bo to come (most of the time) when she starts barking and treat her really good when she does so that helps to redirect her. When all else fails, we also use a squirt bottle with water to get her attention and let her know that the barking is unnecessary. She HATES it, but it's the only thing that I can use at a long distance.
I wish I could leave her alone outside, where I know she would prefer to be, but since I have to live in this neighborhood for the time being (until I can afford a larger piece of property somewhere with no neighbors!), I've got to figure out what the path of least resistance is.