Seminar Notice

Statistical Laboratory

Iowa State University

DATE AND TIME: Monday November 29, 2004, 4:10 p.m.

PLACE:  319 Snedecor Hall

SPEAKER: Philip Dixon, Iowa State University

TITLE:  Combining information from multiple sources to estimate the probability of a rare event

ABSTRACT

I consider the problem of estimating the probability of rare event.  The motivating example is estimating the probability that an insectivorous plant, the cobra lily, will catch a visiting wasp.  The statistically simplest estimate is based on direct observations of plants, recording wasp visits and their outcome (capture or not).  During 376.5 plant hours of direct observation, 157 wasp visits and 2 captures were seen.  The per-visit capture probability is 1.3% but the relative uncertainty in this estimate is large.  Increasing the precision by additional direct observation is laborious.  Another source of information is the total number of wasps captured during a defined time interval.  This aggregated data are easy to collect but provide no information on the number of wasp visits.

I develop models to estimate visitation rate (visits per unit time) and per-visit capture probability by combining detailed and aggregated data.  Simple models assume constant rates; other models allow rates to be functions of plant characteristics.  Inference is by maximum likelihood.  By evaluating asymptotic relative efficiency, I show that combining data increases the precision of the estimated visitation rate when the capture probability is large.  When the capture probability is small, combining data increases the precision of the estimated per-visit capture rate.  The increase in precision can be substantial.  For the cobra lily data, combining data provides the same

precision as over 1700 plant-hours of direct observation.

COFFEE: 3:45 p.m., 104 Snedecor Hall