You might have thought to hide Ribbon from the Anonymous users due to security reason,
In SharePoint 2010 it was simple to modify the master page and that's done, In SharePoint 2013 there has been some changes and we no more need to modify the master page directly, every thing is simplified in 2013 and we just need to modify the concern html page and that should be done.
Every master page in 2013 would have it concerned html page eg for Seattle.master we have Seattle.html
for oslo.master we have oslo.html page which in turn controls the master page and its tags.
Html page has tags that start with <!--MS:--> and <!--ME:--> that show markup inside these tags and in some cases what you would find in the final corresponding master page.
So lets get to the action on what need to done in these html page.
1. Open the html page in SharePointDesigner 2013 or open the site through explorer and open it using your favorite html page editor.
2. Look for <Div Class =”ms-belltown-anonshow”>
3. When we add the following markup enclosed in the <!--MS:--> and <!--ME:—> tags,
<!—MS:<SharePoint:SpSecurityTrimmedControl runat=”server” permission=”AddandCustomizepages”>—>
<Div Class =”ms-belltown-anonshow”>
the design manager will create the corresponding master page with the correct functionality of hiding the Ribbon for an anonymous user.
For list of permission you can refer to