Comp Sci --> Cog Sci

[peanutjellyfish]

How unusual is it for someone to apply to CogSci PhD programs with a research background in artificial intelligence/data science? How should I ask for recommendation letters if my strongest ties are to faculty in Computer Science? I'm mostly interested in computational models of behavior, language processing, decision making, etc. 

My BS is cogsci but since I focused more on the computational side during my undergrad, I feel like I might have more knowledge gaps than someone from psychology or neuroscience. I'm a bit hesitant to try for a MA/MS program first since I'm already pursuing a MS in computer science, and I'd really like to jump into some PhD soon. 

Edit: Edited the title since "CS" can stand for both computer science and cognitive science, haha. 

Edited April 15, 2018 by peanutjellyfish

[Caveat Emptor]

In my experience, having computational skills should go a long way. The field of cognition has embraced computational modelling for the past couple decades and has seen a proliferation in their use in mainstream literature. I would definitely emphasize that when applying. 

[miffle]

Not uncommon in my opinion. I honestly don't think that's a limitation and it can instead be a pretty big asset. I would go ahead and apply to PhD programs with PIs that can fuse your cog sci and comp sci interests. If you're really concerned, you can throw a few MA/MS applications in there as a back-up. In your case, even if I didn't get into PhD programs, I wouldn't do another masters and instead just spend the year working in someone else's lab before re-applying to PhD programs (you'd probably even get paid given your Comp Sci MS).
In terms of letters, you should still ask for them from the people that you worked with most and can speak to your research/lab abilities. I'm not sure if being a professor in the comp sci department would make the letter "weaker" in the eyes of admissions, but I think that would be your best shot. Did you do any comp sci research/projects that intersected with any of the psych topics you listed as interests? If you did, and if a comp sci professor oversaw it, I think that should be sufficient in terms of a "relevant" rec letter.
Finally, if you do consider a psych masters, I can attest that there are a good number of people in funded/thesis based psych masters that came from outside disciplines. Many of them are there because they had a BA/BS in something outside of psych, but I'll occasionally see people that already have a masters in something else. It usually works out for them in the sense that they end up getting into good PhD programs and feel more ready for a psych PhD. However, it's your call whether or not you want to spend another 2 years doing a masters. My opinion is that if it's not funded, I wouldn't go for it.