Biology Reference
In-Depth Information
FIGURE 9.7
Viterbi decoding on simulated data of 400 rolls for the Dishonest Casino Example
9.4
.
The gray background highlights the rolls generated with the unfair die in the simulation.
Digits in bold indicate the unfair die states predicted by the Viterbi algorithm.
Exercise 9.7.
∗
9
Use the
CpG Islands
application in the
CpG Educate
suite to generate
simulated sequences of length of 600 bp with HMM parameters from Table
9.5
with
p
95. (The file
Exercise_9.7.csv
containing the parameters from
Table
9.5
for these values of
p
and
q
is provided for you to load into the
CpG Islands
application). Run the Viterbi algorithm on the simulated data and examine how well
the decoded sequence matches the states of the HMM from the simulations. Generate
several sequences and comment on the outcome. Notice specifically how the maximal
probability path generated by the Viterbi algorithm tends to ignore small gaps between
the island and non-island regions, as already observed at the end of Example
9.6
.
=
0
.
9 and
q
=
0
.
Exercise 9.8.
Experiment with applying the Viterbi algorithm to sequences gen-
erated by the
Dishonest Casino
application in the
CpG Educate
suite. Consider
relatively long sequences of (e.g., 5000 or longer) for different values of the
transition probabilities of the HMM (the four probabilities under the Transitions
heading). Specifically, consider the following types of transition probabilities: a)
transition probabilities are close to uniform (that is, the elements of transition
are close to 0.5), and b) distributions for which the
process retains its current state with a large probability (that is, transition matrices
P
a
FF
a
FU
a
UF
a
UU
matrix
P
=
for which
p
and
q
are very close to 1).
Consider values as large as 0.9999 for
p
and
q
.
For each generated sequence run the Viterbi algorithm and note the general
quality of its performance: Is the decoded sequence generally close to the hidden
sequence generating the simulated data? If there are misses, are those false negatives
(switches to the unfair die in the simulation that have remained undetected by the
Viterbi algorithm) or false positives (predicted switches to the unfair die in places
a
FF
a
FU
a
UF
a
UU
p
1
−
p
=
=
1
−
qq
9
Exercises marked with an asterisk indicate that their execution requires downloads from the volume's
website.
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