RCRP for univariate Gaussian likelihood

Scenario

	k = 1	k = 2	k = 3	k = 4	k = 5	k = 6
Epoch 1	O	O	O
Epoch 2	O	O	O	O
Epoch 3		O	O	O	O
Epoch 4			O	O	O	O
Epoch 5			O	O	O	O

true_KK = 6
TT = 5
N_t = fill(300, TT)

vv = 0.01
true_atoms = [Gaussian1D(kk, vv) for kk = 1:true_KK]

xx = Array(Vector{Float64}, TT)
true_zz = Array(Vector{Int64}, TT)
true_nn = zeros(Int, TT, true_KK)

epoch_chains = Array(Vector{Int}, TT)
epoch_chains[1] = [1, 2, 3]
epoch_chains[2] = [1, 2, 3, 4]
epoch_chains[3] = [2, 3, 4, 5]
epoch_chains[4] = [3, 4, 5, 6]
epoch_chains[5] = [3, 4, 5, 6]

for tt = 1:TT
    n_chains = length(epoch_chains[tt])
    mix = ones(Float64, n_chains)/n_chains
    xx_ = ones(Float64, N_t[tt])
    true_zz_ = ones(Int64, N_t[tt])

    for n = 1:N_t[tt]
        kk = sample(mix)
        kk = epoch_chains[tt][kk]
        true_zz_[n] = kk
        xx_[n] = sample(true_atoms[kk])
        true_nn[tt, kk] += 1
    end

    xx[tt] = xx_
    true_zz[tt] = true_zz_
end

m0= mean(xx[1])
v0 = 2
q0 = Gaussian1DGaussian1D(m0, v0, vv)

init_KK = 3
rcrp_aa = 1
rcrp_a1 = 1
rcrp_a2 = 1
rcrp = RCRP(q0, init_KK, rcrp_aa, TT, rcrp_a1, rcrp_a2)

# sampling
zz = Array(Vector{Int64}, TT)
for tt = 1:TT
  zz[tt] = rand(1:rcrp.K, N_t[tt])
end

n_burnins   = 100
n_lags      = 1
n_samples   = 400
sample_hyperparam = true
n_internals = 10
store_every = 10000
filename    = "demo_RCRP_Gaussian1DGaussian1D_"
nn, components, zz2table = collapsed_gibbs_sampler!(rcrp, xx, zz,
    n_burnins, n_lags, n_samples, sample_hyperparam, n_internals, store_every, filename)

Result

julia> nn
5x12 Array{Int64,2}:
 106  93  100   0   0   0  0  1  0  0  0  0
  76  70   75  78   0   0  0  0  1  0  0  0
  73   1   84  74  64   0  2  0  0  1  1  0
   1   0   67  80  84  68  0  0  0  0  0  0
   0   0   77  69  81  72  0  0  0  0  0  1

julia> true_nn
5x6 Array{Int64,2}:
 93  106  101   0   0   0
 70   76   75  79   0   0
  0   77   84  75  64   0
  0    0   68  80  84  68
  0    0   77  70  81  72

julia> zz2table
5x12 Array{Int64,2}:
 1  2  3  0  0  0  0  4  0  0  0   0
 1  2  3  5  0  0  0  0  6  0  0   0
 1  6  3  2  4  0  5  0  0  7  8   0
 6  0  4  1  3  2  0  0  0  0  0   0
 0  0  8  4  9  3  0  0  0  0  0  10