A friend of mine was followed by a bear in Yellowstone National Park. Apparently, the bear just wanted to walk on the same trail as him. He climbed up a hill and the bear just kept walking.
My uncle went hunting with three other guys and they were attacked by a cougar who had been stalking them. Fortunately, all four guys had guns. The result was Humans 1, Couger 0.
Personally, I don't see a reason to be in a place where animals could stalk you.
Here's an idea: Let's go to the arctic circle and watch polar bears. I probably look like a chicken nugget to a polar bear.