You don’t really need a large caliber, but it doesn’t hurt.I was hiking in the Green Mountains a few weeks ago and came across a couple guys filtering water by a stream. One was shirtless and had a 50 cal Desert Eagle on a chest holster. For big game protection, a large caliber pistol on a chest holster seems like a good combo.
This is a neat analysis of firearm usage in self defense against bears, using actual data.
Defense Against Bears with Pistols: 97% Success rate, 37 Incidents