As a sort of follow up to a previous question, what is advice you would give for telling my MSci advisor I am switching disciplines (pure maths to statistics) for doctoral work? I will presumably ask him for a letter of recommendation. I do not want to come across as ungrateful for his work with me, but the direction of my current research with him has come to bore me. How do I tell him that is a major reason I am switching disciplines? Do I even need to disclose such? I am closing in on completing my work with him, so anything dealing with changing advisors right now is not an option.
In many countries in Europe (France for example), statistics is a part of the Maths department. Theoritical statistics uses a lot of sophisticated mathematics, like measure theory, or functional analysis. A PhD in applied statistics would probably require a serious theoritical research, together with modelisation and programming.
So you should not be ashamed to switch to statistics. Tell your advisor this is not because of him, but due to your personal interest. Excellent scientist are driven by passion!
You may start the conversation by telling your advisor you're switching to physics. If he survives the shock, tell him you were joking and you are "just" going to statistics ;)