sample_tables.m

% function stateCounts = sample_tables(stateCounts,hyperparams,beta_vec,Kz)
% Sample the number of tables in restaurant i serving dish j given the mode
% sequence z_{1:T} and hyperparameters. Also sample the override variables.

function stateCounts = sample_tables(stateCounts,hyperparams,beta_vec,Kz)
   
% Split \alpha and \kappa using \rho:
rho0 = hyperparams.rho0;
alpha0 = hyperparams.alpha0_p_kappa0*(1-rho0);
kappa0 = hyperparams.alpha0_p_kappa0*rho0;

N = stateCounts.N;

% Sample M, where M(i,j) = # of tables in restaurant i served dish j:
M = randnumtable([alpha0*beta_vec(ones(1,Kz),:)+kappa0*eye(Kz); alpha0*beta_vec],N);
% Sample barM (the table counts for the underlying restaurant), where
% barM(i,j) = # tables in restaurant i that considered dish j:
[barM sum_w] = sample_barM(M,beta_vec,rho0);

stateCounts.M = M;
stateCounts.barM = barM;
stateCounts.sum_w = sum_w;