Thursday, December 08, 2011

My "prior" brain has become Bayesian "posterior" mush

Wow, the months sure fly by. It seems like only days ago that I was trapping raptors during fall migration and performing my initial analysis on my goshawk season data. However, I have been very busy and have accomplished a great deal.
The most significant chunk of my time has been devoted to my research annual report. My agreement with the Forest Service requires me to submit an annual report of my study findings. Back in September, I provided a short report which included the status of our nest searches and general goshawk productivity, but much of the analysis came afterwards. By the end of the year I will submit a full report of my results. Before completing the report, I had to watch 3 months worth of nest camera footage and catalog all of the prey items. That was a pretty big time investment. Then came performing the statistical analysis and writing the report. While I could submit a report that just addresses the key questions the Forest Service is interested it, I chose instead to provide a complete report of all the work we performed which includes their key questions as well as the core and secondary questions of my thesis. Additionally, I had the option to submit the results in a general report format, but I chose instead to structure it as a full scientific paper or thesis. This work up-front will greatly streamline my effort when I get around to writing my thesis after my second field season. As a result, it took a lot of time to prepare. I am happy to say that I have submitted a draft to the Forest Service for their review and am awaiting the feedback. In total the document weighs in at 61 single spaced pages! However, I do include lots of photos and detailed maps of each goshawk territory.
The next chunk of my time has been working to figure out Hierarchical Bayesian Analysis. This has been a real challenge. It is not just learning a new statistical procedure, but instead requires a whole new philosophy and approach. As with many tools, the challenge isn't so much in learning the general concepts, but how to apply those general concepts to real problems you are trying to solve. Then, once you have solved the real problem, how do you know it's right? There is no one looking over my shoulder to point out the mistakes. They will all read my report expecting me to be the expert and to educate them. I still have a ways to go...
I am pursuing Hierarchical Bayesian Analysis to address two primary issues I have in my project structure that somewhat violate the assumptions of the frequentist procedures I have used so far. Not to get too alarmed, many papers have been published with these issues, but the right approach is to address them head on. In fact, most published papers have these issues, and only a few recent papers have addressed them. The first significant issue is that I classified historical goshawk territories as "occupied" or "not-occupied" dependent upon whether our search found goshawks nesting there. Of course, if we found a goshawk sitting on a nest, that is an absolute observation. But what about the territories where we did not find goshawks? I cannot say with the same certainty that they were not breeding there. In fact, my procedures have been shown by others to only be 70-90% effective at detecting nesting goshawks. The result is that I am reasonably confident that we missed occupied goshawk nests. Some may even have failed and were abandoned before we entered the field. Yet, they should be classified as occupied if nesting was initiated this season. Bayesian analysis will help me include the detection probability - or the probability that there are "false negatives" in my data.
The second issue is that I am using statistical procedures to produce an estimate of prey abundance in each goshawk territory. While the procedures provide a maximum likelihood value for prey abundance, the values have very wide confidence intervals. They are much more variable than point measurements. The frequentist model fitting procedures I have been using these values in assume a higher precision than this and also assume the error values are roughly normally distributed. These are weak assumptions at best. Those that use these procedures point out that the procedures are "robust" to minor violations to these assumptions. But how minor are they really? The Bayesian approach should help me to address these two issues.
My approach so far, as suggested by our department statistician, is to recreate my frequentist analysis using Bayesian methods. This is possible by building all of the frequentist assumptions into the Bayesian model as priors. Seems simple enough, but oh no... New procedures, new tools, tool integration, and the same old issue - I have to stop thinking about statistics in the same way... It's hard to break a mental model I have lived with for more than 25 years! Yesterday, I was finally successful. I have now recreated my frequentist analysis using Bayesian methods which builds confidence in the tools and the approach.
The next step in the process is to start modifying the assumptions. My response variable isn't normal it's actually a beta distribution. My prey abundance values aren't normal, but instead are gamma distributions. Can I use a single gamma distribution as the "prior", or are they different for each territory (requiring a heirarchical model). I believe I will end up with the latter. We will see where this continued journey takes me!
Oh yeah, I am also taking and teaching classes. My favorite class of my encore educational career so far has been Behavioral Ecology. The whole class has been fascinating, but my class project involved further depth in sex-ratio manipulation and sex-biased parental investment among various species. Last night I presented a paper on sex-biased filial infanticide (female Eclectus parrots killing their second-born male offspring when nesting is poor quality nest hollows). Fascinating stuff!
Moving forward, I am starting to get excited about year two of my study. I received word last week that it will be funded for another year! Many of my procedures will be the same as last year, but I will need to redesign a few of them. My rock-star field assistant is interested in another year as well. I can hardly wait!

1 comment:

Unknown said...

You just proved to me once again that I don't like behind the scenes statistics. I prefer the fancy understandable charts at a glance. I barely scraped by my statistics class for my business minor in college, but have two close friends who are professional statisticians - God bless 'em.