Qualifications for PhD Programs Yann LeCun mentioned in his AMA that he considers having a PhD very important in order to get a job at a top company.

I have a masters in statistics and my undergrad was in economics and applied math, but I am now looking into ML PhD programs. Most programs say there are no absolutely necessary CS courses; however I tend to think most accepted students have at least a very strong CS background. I am currently working as a data scientist/statistician but my company will pay for courses. Should I take some intro software engineering courses at my local University to make myself a stronger candidate? What other advice you have for someone applying to PhD programs from outside the CS field?  

edit: I have taken a few MOOCs (Machine Learning, Recommender Systems, NLP) and code R/python on a daily basis. I have a lot of coding experience with statistical languages and implement ML algorithms daily. I am more concerned with things that I can put on applications.
If I were you I would take a MOOC or two (e.g., Algorithms, Part I, Algorithms, Part II, Functional Programming Principles in Scala), a good book on data structures and algorithms, then just code as much as possible. You could implement some statistics or ML algorithms, for example; that would be good practice for you and useful to the community.

For a PhD program, however, I would also make sure I were familiar with the type of maths they use. If you want to see what it's like at the deep end, browse the papers at the JMLR. That will let you calibrate yourself in regards to theory; can you sort of follow the maths?

Oh, and you don't need a PhD to work at top companies, unless you want to join research departments like his. But then you'll spend more time doing development, and you'll need good coding skills...