Mixed Model and Bayesian Approach

A happy new year 😁  From the end of last year through now, I catch a cold...  I have cough, nasal congestion etc... But, it is getting better day by day!

Anyway, this is an article to summarize what is the difference between Bayesian and mixed model approach.  Honestly speaking, I confused how to use these two because I felt these are similar... 

Recently, I found a good book to explain these two approaches (Demidenko, 2004) and summarized them.  In the book, these two are hierarchical statistical model, but the number of parameters for each approach is different.  For mixed model, additional parameter(s), tau (red in the below slide), includes in the model.  This makes sense to me😄

Reference

Demidenko, E. (2004) Introduction: Why Mixed Models?, in Mixed Models: Theory and Applications, John Wiley & Sons, Inc., Hoboken, NJ, USA. doi: 10.1002/0471728438.ch1.