Department of Statistical Science
Duke University
presents:
Bruno Sansó
bruno@stat.duke.edu
Duke Statistics - Duke University and University of Simón Bolívar
"Redesigning a Network of Rainfall Stations"
Abstract: We consider a network of rainfall stations scattered over a region such that the latitude and longitude of each of the stations is known. For each station we have a set of observations consisting of annual rainfall recorded in millimeters of water over a period of several years. Since we are not willing to consider a serial correlation between rainfall corresponding to different years, we will suppose that the observations at a given location are exchangeable.
Let z be a vector consisting of all the observations, we assume that z follows a normal distribution with a mean that considers a linear relationship for functions of the location of each station and a certain parametric expression for the variance covariance matrix.
Suppose now that we have been asked to reduce the number of stations to decrease cost but maintain accuracy, we then consider a utility function that takes into account both the accuracy of the estimates of rainfall made by the model and the cost of running a given station.
To find interesting designs under the given utility function, we use a stochastic search based on a MCMC simulation over designs d. The MCMC is defined such that the stationary distribution is proportional to the expected utility u(d). We will discuss details of the definition of such schemes. Roughly speaking, the desired optimal design is the design which is most frequently generated in the MCMC simulation. The basic of the rationale is similar to simulated annealing schemes.
September 19, 1997
4:00 pm - 5:00 pm
116 Old Chem Building Any questions concerning the seminar may be addressed to Cheryl McGhee @ [919] 684-8029 or e-mail cheryl@stat.duke.edu. PLEASE contact the author(s) directly for reprints etc.