The Two - Way Likelihood Ratio ( G ) Test
نویسنده
چکیده
These integrations can sometimes be performed analytically, or using some numerical integration techniques. However, we will focus instead on a simple heuristic method which is related to the χ statistics discussed above. Note that David MacKay [3] explicitly assumes the parameters have an ’intrinsic’ arity to them (multinomials with an intrinsic number of bins). This assumption may not be always correct, and in fact, may lead to incorrect assumptions. Now suppose that the hypotheses are multinomial probability distributions HR = {r1, . . . , rN}, with the constraint that ∑ i ri = 1, and each ri corresponds to some range (bin) of the data xR (and similarly we have si for HS), then the likelihood ratio can be written as a sum over the N bins by grouping terms in Equation 1 into the bins: ∑
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