Amazon is a wonderful company with legions of today's brightest minds in their employ, and with this reputation, they are understandably choosy in who they hire. To account for this, the application and interview process at Amazon is labyrinthine. I applied online, and then had a phone screening, an on-demand video interview, a phone interview, another phone screening, and then a 6-hour day of interviews at Amazon's headquarters in Seattle. Despite the immense length of the process, though, I would rate it as an extremely positive experience, even and especially the day of interviews, which flew by.
A few things to be aware of for the interviews: Amazonians dig, and dig deep. What that means for the interview is that they will ask you a situational question, either about your background or about a hypothetical business problem, and then listen to your answer. They will then continue to probe you on details about that situation for at least 10 or 15 minutes; this applies regardless of how they liked your initial answer. Be very careful in picking your initial answer, because if you, for instance, pick a situation from your background that isn't the best fit or about which you don't have enough details, you will still have to come up with myriad answers regarding that situation.
For this position in particular, be sure you can work with data, not just in the abstract or in details about your background, but in Excel form, and in mass, as you will have a skills assessment with a very short timeframe to analyze a good amount of data.