CARIFORUM and UK EPA Study

3.00 3.25 3.50 3.75 4.00 4.25 4.50

.00 .05 .10 .15

-.15 -.10 -.05

25

50

75

100

125

150

175

Residual

Actual

Fitted

Most empirical estimates do not lend themselves to precise parameter estimates. In situations where parameter estimates are misleading or less efficacious because of inadequate or unreliable information we propose probabilistic estimates. We anticipate a useful rendition of Bayesian probability analysis and/or logistic regression for nonparametric insights.

The goal of Bayesian probability estimates is to use inadequate prior information (data) to generate a probability distribution from which useful inferences can be made. Consider Equation 5:

( | )* ( ) ( ) p D T p T p D

( | )

;

f T D

=

(5)

setting T=θ, a probability distribution becomes more meaningful:

( ) ( | )* ( ) . f D f D f d q q q = ò

(6) Equation 6 shows that the posterior estimation is proportional to the product of the likelihood of

( | )

( ) p D T p D

( ), the likelihood ratio

an occurrence, and the prior information; where D is for the available data, and T is for the parameter that estimates the variable of interest. The likelihood

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