I'm currently working on a PhD in cognitive science, but my research and interests straddle the line between cognitive science and mathematics. Right now, I am most interested in pursuing an academic career, and I've begun looking at job openings for postdocs and assistant professorships just to see what's out there (fully realizing those exact positions will be long gone by the time I graduate). I noticed that some positions listed in statistics/mathematics programs seem to fit my overall interests and skills; however, they almost universally state that a PhD in mathematics or statistics is required to apply.
When the time comes to apply for positions, should I even bother applying to the ones where my PhD is not technically among the ones listed on the job opening? Obviously, if my PhD was in a completely different field than the position in question, my chances of getting it would be low. However, what about positions where my research is within the scope of the field in question, even though my PhD is not (e.g., my PhD is in cognitive science, my research deals with statistical approaches to study cognition, and the position is in a statistics department)? Would I be disqualified on a technicality?