4-1.4 Changing odds to weights.

To simplify the mathematics further it is possible to take the logarithm of the adjusted odds so as to get field weights. We multiply probabilities together to yield a total probability. The product of the odds is directly proportional to the total probability.

(4.5a)
We add their logarithms together to yield a sum that then represents the logarithm of the product of the probabilities, viz., the odds.

(4.5b)
When we choose to use two as the base of the logarithms, we have a binit weight. The field's weight for agreement (awi) is therefore,

awi = log2 (ai)(4.6)
The field's weight for disagreement (dwi ) is similarly,

dwi = log2 (di)(4.7)
bwi = log2 (bi) = 0(4.8)

If the field values are independent, the principle of independent probilities (cf. 2-2.5) allows us to conclude that the sum of the weights of the odds for each field will be proportional to the probability of them occurring in that combination of agreement, disagreement, and being missing. In this way we add field weights to yield a record comparison weight. Because we use the principle of independent probabilities, it is very important to consider the independence of the data between the fields to be weighted. We discuss this concern in chapter 5.