Nonparametric Bayesian Discrete Latent Variable Models for ...

15
10
5
−0.5 0 0.5
2
1
G 0
0
−0.5 0 0.5
1.5
1
0.5
G 2
0
−0.5 0 0.5
0.4
0.2
G 8
0
−0.5 0 0.5
0.4
0.2
G 32
α=1, G 10000
0
−0.5 0 0.5
3
2
1
3.1 The Dirichlet Process
G 1
0
−0.5 0 0.5
2
1
G 4
0
−0.5 0 0.5
0.8
0.6
0.4
0.2
G 16
0
−0.5 0 0.5
0.15
0.1
0.05
G 10000
0
−0.5 0 0.5
0.03
0.02
0.01
α=100, G 10000
0
−0.5 0 0.5
Figure 3.3: Sequential draws from the generalized Pólya urn. The base distribution G0 is a zeromean
Gaussian with standard deviation σ = 0.1. Plots on the first four rows show
the evolution of Gn with increasing sample size for the concentration parameter
α = 5. The continuous red curve shows the contribution of the base distribution,
and the crosses show the atomic measures on the sampled points. For visualization,
we show δθ(·) with a unit length line. Note that the influence of the base distribution
vanishes as the sample size increases, and Gn converges to a discrete distribution.
The last row shows Gn after 10000 samples for α = 1 (left) and α = 100 (right),
showing that for large α, the draws concentrate around G0. (The samples are binned
for visualizing Gn for α = 100.)
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