How can one choose to believe something, or to disbelieve it? Can one choose to believe something one knows is false?
Tough question...
I asked a christian friend if they chose to believe in god and they replied with a suprised "yeah"

, "Duh!", like, how could I imply that they didn't choose. I too, feel like I choose to believe in god.
How?, you ask... I have no idea.
Maybe belief is made up of multiple layers. Perhaps, the very bottom layer, the most basic thoughts on god's existence, cannot be chosen, but as we climb up the layers and get more into the beliefs, they do become choices we have to make, especially when dealing with things that are not evident.
You know what I mean?
Your examples are matters of fact. When talking about god though, they don't apply as well.
Change your question from being about mooses to being about god and answer them for me.
Suppose you are standing by a marsh, and you see a mooseGOD (it's hard to mistake a mooseGOD!). Could you disbelieve in the presence of the mooseGOD by any effort of will whatever?
Isn't it easier to say "yes" when the subject is god and not a moose. If you could say yes, then wouldn't you be choosing to believe if you did believe.
Science fails to recognize the single most potent element of human existence.
Letting the reigns go to the unfolding is faith, faith, faith, faith.
Science has failed our world.
Science has failed our Mother Earth.
-System of a Down, "Science"
He who makes a beast out of himself, gets rid of the pain of being a man.
-Avenged Sevenfold, "Bat Country"