In another question I asked recently about best practices for whiteboarding, there was general consensus that thinking out loud while coming up with the answer was the best strategy.
Indeed, long moments of silence are awkward.
However after recent interviews I have noticed that if my thinking out loud leads to wrong solutions or down the wrong path, that with further consideration I would have seen, interviewers tend to quickly jump in and point out problems with my approach, especially if I stop to pause for a minute. This was not an isolated case, and happened during more than one interview with more than one interviewer.
The other thing is that after the interview, on a problem I absolutely bombed, when I sat down and sketched out the problem on a piece of paper in silence I was able to sketch out the solution pretty quickly. Thinking out loud ends up with me spending brain cycles on reflecting on how what I say must be registering with the interviewer and in addition there's a fear of recognizing that I've gone down the wrong path and starting over after having written something on the board wastes a lot of time. Once you've started down one path and realize you've written a lot of junk, you can't undo it, whereas if you've thought quietly about it the interviewer wouldn't have seen the mess and it would have been quicker since whiteboarding a bad idea takes up more time than simply considering a bad idea.
I don't want moments of silence but at the same time speaking takes more time, leads to self-consciousness and can lead to interviewer intervention on something I might have figured out myself with just a little more time.