7.3 The non-identifiability of mixture models
The means parameter has shape 2, and from Figure 7.6 we can see that one of its values is around 47 and the other is close to 57.5. The funny thing is that we have one chain saying that means[0] is 47 and the other 3 saying it is 57.5, and the opposite for mmeans[1]. Thus, if we compute the mean of mmeans[0], we will get some value close to 55 (57.5 × 3 + 47 × 1), which is not the correct value. What we are seeing is an example of a phenomenon known as parameter non-identifiability. This happens because, from the perspective of the model, there is no difference if component 1 has a mean of 47 and component 2 has a mean of 57.5 or vice versa; both scenarios are equivalent. In the context of mixture models, this is also known as the label-switching problem.
Non-Identifiability
A statistical model is non-identifiable if one or more of its parameters cannot be uniquely determined. Parameters in a model are not identified if the...
