Adaptive Sampling with a Bayesian Approach

Project Abstract Adaptive sampling is a sampling design in which the selection of units in the sample may depend on the values of the variable of interest observed during the survey. The sampling intensity may be increased in the vicinity of high observed abundance with an adaptive sampling method. The method provides an efficient way of sampling when the population has a clustered structure and is also applicable to clumped or aggregated distributionsas as are often found in sampling plants, animals pollution sites and certain problems in epidemiology. Without making specific assumptions about the distribution of the population, various estimators had been proposed for adaptive cluster sampling. (In adaptive cluster sampling, an initial sample of units is selected and whenever the value of the variable of interest satisfies a specified condition, the neighbouring units are added to the sample.) These estimators are unbiased and can be used in very general settings. However, in those cases where we do have existing prior information about the population of interest, it may be possible to derive more efficient estimators using a Bayesian analysis. Also, a Bayesian analysis yields one distribution (the posterior distribution) for the unknown parameters, and from this distribution a large number of questions can be answered simultaneously. For instance, one can obtain accuracy measures for the estimates with little extra effort. In this project, we are going to use a Bayesian approach for estimating the population total, which is an important practical problem.