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Imagine you would like to use a simple Gibbs sampling to resample from a joint probability distribution which is difficult to model (but you know all the conditionals Pr(X_i|X_1,...,X_{i-1},X_{i+1},...,X_N), for i=1,...,N, hence the Gibbs sampling). At the end, you would have a set of many drawn vectors of variables (x_1^(k),x_2^(k),...,x_N^(k)), for k=1,...,K. Imagine now you would like to assign a vector of variables (y_1^(k),y_2^(k),...,y_M^(k)) to each of the already drawn vectors. You have some conditional probabilities like Pr(Y_j|Y_1,...,Y_{j-1},Y_{j+1},...,Y_M,X_1,...,X_N). Again, modelling joint distributions is difficult. Do you think it can work a Gibbs sampling with these conditionals by inserting sequentially the previously drawn x_i^(k) and, after discarding some steps, collecting the sampled y_j^(k)? Otherwise, do you have a strategy to apply in these cases? Thanks! |
