When we use the maximum likelihood method in complicated scenarios, the likelihood value corresponding to the maximum likelihood estimate is often quite small.

Question

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In complicated scenarios, the likelihood value at the maximum likelihood estimate (MLE) can indeed be quite small due to the complexity of the model and the high dimensionality of the parameter space, which can lead to a diffuse likelihood function over a wide range of parameter values.

When We Use the Maximum Likelihood Method in Complicated Scenarios