After you have setup a new BizTalk server and start deploying BAM Activities, in this case Microsoft.BizTalk.ESB.BAM.Exceptions.xml which has a Cube that needs to be deployed into the BAM OLAP Database, you can get this error:
To fix this error, you need to find the logon that was trying to access the BAMStarSchema database, in this case ‘NT SERVICE\MSSQLServerOLAPService’ (this is the default account for OLAP in the SQL Install)
Add ‘NT Service\MSSQLServerOLAPService’ as a SQL Logon
Give this account db_datareader for the BAMStarSchema database
Re-Run the BAM Deploy
Problem Fixed