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Reversible jump
In recent years a method developed by Green [1] allows simulation of the posterior distribution on spaces of varying dimensions. Thus, the simulation is possible even if the number of parameters in the model is not known. Let Additional recommended knowledgebe a model indicator and the parameter space whose number of dimensions dm depends on the model nm. The model indication need not be finite. The stationary distribution is the joint posterior distribution of (M,Nm) that takes the values (m,nm). The proposal m' can be constructed with a mapping g1mm' of m and u, where u is drawn from a random component U with density q on . The move to state (m',nm') can thus be formulated as
The function must be one to one, differentiable, and have a non-zero support so that there exists an inverse function that is differentiable. Therefore, the (m,u) and (m',u') must be of equal dimension, which is the case if the dimension criterion
is met where dmm' is the dimension of u. This is known as dimension matching. If then the dimensional matching condition can be reduced to
with
The acceptance probability will be given by where denotes the absolute value and pmfm is the joint posterior probability
where c is the normalising constant.
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This article is licensed under the GNU Free Documentation License. It uses material from the Wikipedia article "Reversible_jump". A list of authors is available in Wikipedia. |