From a small northwestern observatory…

I had the very real pleasure of speaking at the Appraisal Institute’s annual meeting this past July in Dallas, and indeed I’ve been asked to speak there 3 of the past 4 years — a great group and a very well-done conference.  My topic this year was on “Practical Statistics for Practicing Appraisers”, and given the need for continuing education credit, my talk was scheduled for two hours.  Unfortunately, two hours is either w-a-a-a-a-a-y too much time, or not nearly enough, depending on what you want to do with it.

About the only thing I could do was touch base on a dozen or so different useful topics, talk about the highs and lows of each, and point the audience in the right direction to get more information.  One topic I wish I’d spent more time on was Bayesian Statistics, a little-known and under-appreciated branch of statistical inference which, in fact, has significant every-day impacts on how we analyze (or at least SHOULD analyze) data.  For example, let’s say that I want to determine the house price trend in a particular town, and have no idea what that trend looks like.  I’ll want to construct some sort of “best linear unbiased estimator” (such as a time-series regression) to help me sort all that out.

However, what if afterwards, in that same town, I’ve already measured the overall property trends, but now I’m told that half of the town is known to be contaminated.  Do I still want to use the same estimators, or should my methodology be informed by what is now “prior knowledge” about both the existence of the contamination and the overall price trend in the town?

This use of prior knowledge falls into the category of “Bayesian Statistics”, or “Bayesian Inference”, developed by early-18th century theologian and mathematician Sir Thomas Bayes.  In short, Bayes noted that our inferences could be improved by the existence of prior knowledge.  What’s more, when we’re conducting a Bayesian investigation, our data gathering is anything but random, since we’re seeking data based on our prior knowledge of the situation.  In the contamination matter, I may want to look at price trends for homes in the contaminated neighborhood versus price trends for homes in the non-contaminated neighborhood.  Naturally, I’ll only focus my attention on properties that have actually transacted, which leads to a common problem in this sort of analysis where properties that have not transacted (which may contain different information) are not part of the data set.

Unfortunately, a lot of practical appraisal — particularly in the residential setting — is heuristic, and over-reliance on “prior knowledge” can lead to a level of sloppiness.  That said, a rigorous application of Bayes’ principles, and careful analytical techniques, can allow appraisers to actually develop statistical measures for their valuation work.