I'm not at all active on these forums, but I thought I would chime in. I am currently a senior in mechanical engineering and was accepted to several computer science PhD programs for this coming fall.
The reason I think I was accepted is because of excellent recommendations and a plethora of research projects that involve programming. While my background is in mech engineering, I have done of lot of engineering club and research projects where I end up programming some algorithm or putting together some software system. It also helps that my interests (robotics, computer vision) are very interdisciplinary. I actually found during my visits that many students didn't come in with a major in computer science. Several people were computer engineering (essentially half electrical engineering and half CS) or other STEM majors.
The fact that you have a background in statistics and want to go in to an area like machine learning should push your application. It's not like you want to do CS theory where a computer science background is vital. As long as you are confident in your programming abilities and have enough math background then it shouldn't be a big deal.
