Bayesian Approach

• Include judgmental information to arrive at a better estimate probability/fraction

  • i.e., know there was a release of gasoline from a tank

• Assign a mean fraction of soil above a target level and a variance on that fraction for each source area

  • for example, areas expected to be above a target level are assigned a fraction of 0.75 and a variance of 0.25

• Update the fraction and variance using available data in that region

  • Use a beta distribution: fp(p) = G(q+r)/[G(q)*G(r)] * pq-1 * (1-p)r-1

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The Bayesian Approach takes the binomial method one step further by including information about prior activities in a source area. For instance, if we knew a large amount of gasoline was released from a storage tank, we would expect the soil concentrations for benzene in that area to be above a target level. We can assign a value for the fraction of soil we expect to be above the target level along with a variance on that fraction. This fraction is identical to the probability I was referring to earlier. For example, in areas where high levels are expected, we can assign a fraction of 0.75 and a variance of 0.25. We can then update the fraction with existing data measurements. We use a beta distribution for this step.