Overview of Bayesian Approach

Johnson (1993, 1996, 1997) has shown that a combination of bayesian and geostatistical techniques can be effectively used in an adaptive sampling or iterative sampling approach that guides characterization of a site. Johnson (1996) contains the best available description of the technical aspects of the methodology.

The first step in the process is to create a grid over the area of interest. In each grid cell block, professional judgment and prior information is used to estimate the probability that if a sample were taken at that point, the result would exceed a specified threshold. At the same time, some idea of how confident one is in this prediction is also given. After this probabilistic soft data (referred to here as professional judgment) is available, hard or sampled data may be used to update the probability in each grid cell that a sample taken there would exceed a threshold value. Note: this grid will later be the same grid on which the geostatistical methods are applied.

In particular, one is estimating

image\v4ht0320.gif , image\v4ht0321.gif,

where ">0 and $>0 are the parameters of a Beta Distribution. Here, : is the probability value and F is the measure of uncertainty about that probability value. The estimates of : and F may or may not be based on previously collected "hard data" taken during remediation control, characterization, or scoping data. They might be based only on general knowledge, such as the knowledge of a spill or the particular geology of the site.

The values of : and F that are entered are converted to " and $ values by solving the following equations:

image\v4ht0322.gif andimage\v4ht0323.gif.

In the current implementation, values of : and F can result in negative values of " and $. For these instances, SADA sets " and $ equal to a small numerical value. Issues about controlling non-negative values have come out of developing this prototype module and will be addressed in the next version.