How to track reboots in Jelly Bean Samsung Galaxy Nexus (Verizon) with Android 4.1.1 (unrooted).

I seem to be having unusually frequent reboots of my phone; sometimes multiple times in a day. Certainly much more frequent than with Ice Cream Sandwich (4.0.4).

Additionally, my battery life seems to be lower since the upgrade from 4.0.4. (It might be my imagination, but it might be running hotter than I remember, too.)

I've been looking for some common denominator but I'm baffled.

What can I do to try to find out what is causing these crashes?

(No suggestions that require rooting, please.)
System Tuner looks like it could help you figure out what's going on. Excerpts from the app's description:


  
  Display log(cat) for all/one process (even on JellyBean Android 4.1)  
  Record (optionally at boot) activities in the background  
  Record all apps or all processes  
  Allows analyzing past recordings without limits
  


I didn't try it for this special purpose, but the description suggests you can check what was going on when the device went down even afterwards: which processes were running, memory and CPU status, and more. As it is able to read system logs fine even on JellyBean, it should be able to give you the information needed to figure out what is going on.