About 6 years ago I installed a good quality, Panasonic Whisperfit ceiling fan:

This was a remodeling project where I installed a new half bath, including all-new wiring. I'm fairly knowledgeable about wiring and it was installed properly and there have been no problems until today, when my significant other called me down to the bathroom because the fan seemingly started up by itself and was very loud; she swears she hadn't been anywhere near the switch. I tried to turn it off using the switch, but it wouldn't seem to turn off. Then I flipped the GFCI breaker that protects the bathroom, and this switched it off. After resetting the breaker, the fan turned off and on normally via the wall switch, though it seems a bit louder than I remember. It's connected to rigid, 4" ducting, and it's only a 3' run to the outside wall exhaust. It's also a bathroom that isn't high use, so the fan is not frequently turned on. Lastly, there is only one cable entering the connections box in the fan, which is the cable running directly from the switch in the wall. And I opened up the switch box -- which is 3-gang with a switch for the fan, a switch for the overhead lights, and a receptacle -- and all the connections in the box are tight and there are no loose wires under the wire nuts.

I'm stumped. Any thoughts would be appreciated.