A colleague of mine caught and tagged 57 birds (white storks) with a GPS collar that records the location of the bird and the height it is flying at. One of the goals of the study is to analyse how white storks behave in the vicinity of power lines. Their hypothesis is that white storks will fly higher in the vicinity of power lines to avoid collisions. My colleague started by doing a linear model relating flight height and distance to power lines and add by adding varying effects for individual storks:
flight_height ~ normal(mu,sigma) mu<-a[stork_id]+b[stork_id]*distance_power_lines
but found no pattern.
I was wondering if there is a better (and Bayesian) approach for this problem that I can recommend to my colleague. It occurred to me that Bayes’s theorem might be useful here.
Power lines are 40 m high and we can assume that for a white stork to fly over a power line it will have to be flying at an altitude > 40 meters within 100 meters of a power line. I thought of formulating the problem like this:
P(height > 40m / distance < 100 m) = (P(distance<100m/height > 40m)*p(height > 40m)) / (distance<100m)
First of all, is this formulation right?
If so, how can I “convert” this formulation in Bayesian regression model that can be run in STAN? I am asking for a regression model because there are other covariates that may influence bird behaviour in the vicinity of power lines, e.g.: bird age (older birds may be more careful around power lines and fly higher than younger ones) and habitat (power lines in prairies are more visible than on forests).
Thanks for the help.