SSAS: Powershell to replace a group member in a role

There was a question in the SSAS forum recently on how to replace one group name with another within the membership of a number of SSAS roles in a number of databases. While you could possibly do this with XMLA it would be tricky as you have to re-submit the whole membership list, you can't just add/remove single members. The easiest way to do this is to write something using the AMO library and in my opinion the easiest way to write a script for AMO is using Powershell.