## How the LogLikelihood Ratio Criterion Works

### Likelihood is "the probability of the data."

It is proportional to the probability that the experiment turned out the way it did.

So some POD model parameters are more likely than others because they explain the inspection outcome better than other values.   We choose the "best" parameter values, i.e. those that maximize the likelihood, called not surprisingly, "maximum likelihood parameter estimates."

The most likely parameter values are the "+" but other values are also plausible, although less likely.  That (x, y) pair produces the best GLM (Generalized Linear Model) fit of the data, shown as the black line in Figures 2 and 3.

Each point along the 95% confidence contour of the loglikelihood surface produces a GLM line (Figure 2) and its corresponding POD(a) fit (Figure 3).

The triangle identifies the (x, y) pair (location and shape, and ) whose line is associated with a90/95.

Figure 1 - LogLikelihood Ratio Surface

 Figure 2 - Logit (and POD) vs. Size Figure 3 - POD vs. Size