Likelihood of the cause, given the observations
As we have just seen, if we assume some value of q, where q is the p(heads),
we can calculate the probability of the observations HHTHT given q.
We can use this fact to help us work out the value of q when this is unknown.
Say I work out the probability of the observations, HHTHT, for every possible value of q
from 0 to 1 in steps of 0.01.
Let's try this using the preprepared MATLAB code in script 'UncertaintyTutorial1.m'.

Open the file 'UncertaintyTutorial1.m' in Matlab

Run section 1 only
HELP!
You should have a plot a bit like this
?
From this plot, we can clearly see that the the observations, HHTHT, were most probable given
a certain value of q  what is that value?
?
0.6  why should this not surprise you?
?
Because if the true value fo q was 0.6, the coin should come up heads 3/5 of the time 
the exact ratio observed in the sequence HHTHT.
You may recall from the lecture that there is a mathematical relationship between
 The probability of the data given the parameters of the environment,
in this case, p(HHTHT  q)
 The likelihood of the parameters, given the data we observed,
in this case p(q  HHTHT)
Namely: p(q  data) = p(data  q)
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