The toilet in my master bedroom intermittently begins to fill on it's own, as if the tank hasn't drained all the way. It happens long after the toilet has been flushed, and can happen at least 10-20 times per day. There is not much water in the toilet to begin with, and when it fills on it's own, it only runs for about 3-4 seconds, but I can see and hear the water running. There are no leaks that I can feel or see. Any suggestions or thoughts?

Probably a leaking flapper or flapper gasket. Put some food coloring in the tank, watch for a few minutes and then tell us if you see color. In the meantime, shut off the stop valve on the water line to save water and turn it back on when you need to flush. If it is "mystery" flushing as much as you say, you are certainly wasting water.

After you check the flapper check the water level in the tank. It should be about 1/2" under the white overflow tube when the tank's filled/ If higher then that adjust it lower. Good luck, Tom