restricted_gibbs: Restricted Gibbs scan to update assignment indicators in S.
In zhenkewu/rewind: Reconstructing Etiology with Binary Decomposition

Function to perform Gibbs scan only for the observations associated with either i or j (randomly chosen), but not including the cluster indicator for i or j. This function does not change the cluster observation i or j currently is in, because the restricted Gibbs scan only updates other observations in S by randomly assigning them to the cluster with i or j.

restricted_gibbs(
  Y,
  zsa,
  zsb,
  cia,
  cib,
  cja,
  cjb,
  ni,
  nj,
  i,
  j,
  S,
  ns,
  b,
  active,
  Q,
  p,
  theta,
  psi
)

`Y`	multivariate binary data (row for subjects, column for dimensions)
`zsa`	cluster assignment indicators prior to updating (transition from in MH)
`zsb`	cluster assignment indicators after updating (transition to in MH; same below.) both zsa and zsb will be set to zs when active is true, because we want the zs to be modified/updated.
`cia, cja`	cluster indicator for subject i,j prior to updating
`cib, cjb`	cluster indicator for subject i,j after updating
`ni, nj`	the number of subjects clustered with i (j) - including i (j).
`i, j`	two distinct subjects' indices
`S`	the set of indices clustered with either i or j (including i and j)
`ns`	size of S
`b`	gamma in the Dirichlet distribution in MFM.
`active`	TRUE for performing a split update (both updating cluster indicators and computing the transition probabilities), FALSE otherwise (only for calculating proposal density; used in q(Z\|Z_merge) = q(Z\|Z_launch)).
`Q`	a Q matrix of dimension M by L
`p`	a vector of machine (factor) prevalences of length M
`theta`	a vector of true positive rates of length L
`psi`	a vector of false positive rates of length L

log_p the log probability of transitioning from zsa to zsb (product of all subjects in S);
ni,nj the number of subjects assigned to cluster for i,j
zsb updated assignment indicators for subjects in S