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+function state = sample_mdp(prior, trans, act)
+% SAMPLE_MDP Sample a sequence of states from a Markov Decision Process.
+% state = sample_mdp(prior, trans, act)
+%
+% Inputs:
+% prior(i) = Pr(Q(1)=i)
+% trans{a}(i,j) = Pr(Q(t)=j | Q(t-1)=i, A(t)=a)
+% act(a) = A(t), so act(1) is ignored
+%
+% Output:
+% state is a vector of length T=length(act)
+
+len = length(act);
+state = zeros(1,len);
+state(1) = sample_discrete(prior);
+for t=2:len
+  state(t) = sample_discrete(trans{act(t)}(state(t-1),:));
+end