Information Theory, Inference, and Learning ... - MAELabs UCSD

Copyright Cambridge University Press 2003. On-screen viewing permitted. Printing not permitted. http://www.cambridge.org/0521642981
You can buy this book for 30 pounds or $50. See http://www.inference.phy.cam.ac.uk/mackay/itila/ for links.
368 29 — Monte Carlo Methods
(a)
12
10
8
6
4
2
0
40
35
30
25
20
15
10
5
0
90
80
70
60
50
40
30
20
10
0
(b) Metropolis
100 iterations
0 5 10 15 20
400 iterations
0 5 10 15 20
1200 iterations
0 5 10 15 20
12
10
8
6
4
2
0
40
35
30
25
20
15
10
5
0
90
80
70
60
50
40
30
20
10
0
(c) Independent sampling
100 iterations
0 5 10 15 20
400 iterations
0 5 10 15 20
1200 iterations
0 5 10 15 20
Figure 29.12. Metropolis method
for a toy problem. (a) The state
sequence for t = 1, . . . , 600.
Horizontal direction = states from
0 to 20; vertical direction = time
from 1 to 600; the cross bars mark
time intervals of duration 50. (b)
Histogram of occupancy of the
states after 100, 400, and 1200
iterations. (c) For comparison,
histograms resulting when
successive points are drawn
independently from the target
distribution.