I know several folks here who have Anatolians. I would never have one. They bark all night at nothing. They can't seem to stay on the property. I know someone who has a couple that have the run of about 10 acres, that is all fenced- their other dog, a Mastiff, never left the property while she was alive, but these dogs they have now hunt for ways to escape and off they go- running the neighborhood for hours. They dont seem to the be the brightest crayons in the box either. Are not much good for guarding if they dont stay home! Most folks that I know have had trouble keeping them on their own property and keeping them from barking non stop.
My daughter and her husband have a lab that goes over a five foot fence like it isn't even there; my Anatolian and Pyr/Anatolian cross won't even *try* to go over the four-foot high fence we have for the front barn yard (the rest of the property is five foot high woven fence). I know that the Pyr/Anatolian cross could get out easily if he wanted to-- the first night we had him we put him in a stall and he was out of the stall by morning (four foot solid walls.) We can and do leave the gate open while we are bringing in feed, etc, and the dogs don't go out. It surely depends on each individual dog, but I would think that if a dog were happy and occupied they wouldn't try to leave.
Also, one does need to realize that barking is a very big part of how Livestock Guardian dogs do their job: they bark to warn away potential predators. When we first got our already-adult Pyr/Anatolian, he barked all the time. Constantly. It was driving us crazy. But, he was new here, and he didn't know what was "normal" and what didn't need to be barked at, and what did. He slowly learned, and now he only barks when he feels he needs to warn something off. But yes, if one is considering a Livestock Guardian Dog, one does need to take into consideration that one needs GOOD fencing, and that barking (and very possibly digging) are a part of having that type of dog. They are generally also big dogs and they are going to need plenty of dog food. There are going to be costs for vaccinations, heartworm meds, etc, and they are going to need to be socialized, trained, brushed, toenails trimmed, etc. Mine expect some attention when I go out, though they aren't obnoxious about it, they appreciate a scratch behind the ears. The Anatolian that saved a foal's life last year makes sure that I fulfill my promise of occassional belly rubs.
Livestock Guardian Dogs aren't for everyone. But for me, they are worth their weight in gold.