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Using this locus as the boundary for A means defining A by the condition [sigma] > 0, the common sense normalization for this transparent example.
the MLE, which they refer to as the likelihood principle for normalization.
One class of models for which the normalization problem arises is when the observed data come from a mixture of different distributions or regimes, as in the Markov-switching models following Hamilton (1989).
If this is one's goal, the best approach may be to simulate the posterior distribution of [theta] without imposing any normalization at all, deliberately introducing jumps in the simulation chain to make sure that the full range of permutations gets sampled, and checking to make sure that the inferred distribution is exactly multimodally symmetric (e.
In this case, the structural interpretation dictates the normalization rule that should be adopted, namely [[mu].
However, according to the identification principle discussed in the introduction, this is not a satisfactory solution to the normalization problem.
To illustrate what difference the choice of normalization makes for this example, we calculated the log likelihood for a sample of 50 observations from the above distribution with [[mu].
8, this results almost by force from the normalization p > 0.
Unfortunately, the Wald normalization seems to do slightly worse at describing the distributions of [[mu].
5 normalization in part results from the interaction between the normalization rule and the prior.
It is clear from this discussion that we need to be aware not only of how the normalization conforms to the topography of the likelihood function, but also with how it interacts with any prior that we might use in Bayesian analysis.
A structural VAR typically makes both exclusion restrictions and normalization conditions on [B.