Models of Learning

Developed by
Jill O'Reilly
Hanneke den Ouden
-August 2015

## 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 pre-prepared 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?

?

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)