Philip Dixon
Department of Statistics
Iowa State University
"Combining Multiple Sources of Information to Better Estimate the Probability of a Rare Event"
3:00 Refreshments in 241 Schaeffer Hall
3:30 Talk in 140 Schaeffer Hall
A few species of plants have evolved specialized structures to capture and digest insects. As part of their study of the cobra lily, two biologists collected data to estimate both the frequency of insect visits to cobra lilies and the per-visit probability of prey capture. When data are collected by sitting and watching plants, estimation is trivial. However, this direct observation is time consuming because successful capture is rare. Only 157 visits and 2 captures occurred in 376.5 plant-hours of direct observations. Both the average capture probability and the relationship between capture probability and plant size are imprecisely estimated.
Data on the total number of captures during a defined time period are very easy to collect, but these aggregated data provides no information on the number of visits. I develop Poisson-Binomial models that combine direct and aggregated data to better estimate average capture probability and visitation rate. The models are extended to estimate the relationship between capture probability and plant size. By evaluating asymptotic relative efficiency, I show that combining data sometimes increases the precision of the capture probability and sometimes increases the precision of the visitation rate. For these data, combining data substantially reduces the variance of the estimated capture probability.
