I'm involved in a census at our condo association. We may, for logistics reasons, survey 1/4 of the population per quarter so that we have surveyed everyone by the end of the year, but let's assume we survey everyone at once.
A year later, we survey again. Since we're attempting to cover 100% of the population each year, the results are what the results are each year, right? It wouldn't make sense to run last year's results (prior) and this year's results through Bayes Rule would it?
EDIT: In response to the excellent questions, I'm thinking of a single question on the survey that is asked both years. For example: what percentage of residents believe that the Management Office does a good job of handling complaints? At first glance, this seems textbook-like: you have a prior distribution based on the previous poll, you gather data, use Bayes, and now you have a posterior which in principle better reflects reality than the prior or current data. EDIT2: For this question, I'm assuming that there is no other data: we simply have (anonymous) polling results (and uncertainty) from one question asked in two different polls and wonder if the data for that question can be combined in some manner.
EDIT: As the answers point out, the problem is that the two samples are not independent, regardless of how far apart they are, because many residents will be asked both years. (Which gets me thinking: how independent is "independent"? Do we say that we need a method of choosing respondents that has less than 95% (99%, etc) probability of picking the same respondent twice?)
If we were taking samples from a much-larger population, I can see how Bayes Rule would be helping us to solidify our answers, but in this case... Actually, I'm not sure how using Bayes Rule on data that is evolving over time (polls, say) would work out, since the prior is "out of date" in some sense.
Does it make any sense in a census (attempting to survey the entire population) situation to run the prior census' results and the current census' results through Bayes Rule?
If we only get a 50%, say, response rate would that change the answer to #1?
Does it make sense to use, say, polling data as a prior for polling if we know that the data (opinions) are changing over time? (i.e. aren't priors a statement of prior belief about the current situation, not just arbitrary beliefs at some time in the past?)
EDIT: It appears that once the population's answers are subject to change, we then have to actually model this change (at least accounting for time), at which point we've moved beyond a simple application of Bayes Rule. IS that correct?