As Srujana mentioned, this is not available OOTB but might be achievable with some custom work.
OOTB you could do 2 things:
1. Like Jürgen mentions, a private category that houses the blog for which you could see member metrics in Community Analytics (CA->Content->scope to category->Members tab or use filters in other CA menus). The caveat here is that you will need to create and assign a special role to the members that need to access this category.
2. You could use the new Group Hubs feature and create a Closed or Hidden Group Hub for the members that need access to the blog. You will be able to control membership and have dedicated metrics for Group Hubs in Community Analytics. More on Group Hubs here.
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