My overall question is: Should I prepare new writing sample for a field I'm trying to enter, or submit a published writing sample in my old field (which is very technical)?
I'm trying to transition out of a purely technical position (an academic, postdoctoral position in a field of computational science) into a public policy position.
The specific role I'm now preparing an application for combines some quantitative analytic work (some statistics and data visualization, etc) with a large writing component.
I'm very qualified for the quantitative aspects of the role, and I think I can illustrate from my body of technical/academic work (and my cover letter) that I am also a strong writer.
However, I feel the weak point of my application is the writing sample. I have many examples of technical writing, but much of it is so embedded in mathematical jargon that it would be inaccessible to anyone outside my narrow field. It also does not support my (genuine) interest in focusing on public policy.
I've considered writing a short article (perhaps a book review? essay?) based on a relevant public policy topic. I think this may be a good idea in general, but I'm also anxious to get in an application to this current position. I'm also not confident in my ability to write a pertinent piece here (this is part of the expertise I hope to develop).
Alternately, I'd considered submitting a former grant application (tightly written and somewhat less technical than a paper) or a high-level research overview.
Thank you for any advice.