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

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21.2: Exact inference for continuous hypothesis spaces 297
0.06
0.05
0.04
0.03
0.02
0.01
1 0
0.8
0.6
0.1
sigma
0.4
0 0.5 1 1.5 2
2
0.2
1.5
1
0.5
mean
mean
0
1
0.9
0.8
0.7
0.6
sigma
0.5
0.4
0.3
0.2
Figure 21.4. Likelihood function,
given the data of figure 21.3,
represented by line thickness.
Subhypotheses having likelihood
smaller than e −8 times the
maximum likelihood are not
shown.
Figure 21.5. The likelihood
function for the parameters of a
Gaussian distribution.
Surface plot and contour plot of
the log likelihood as a function of
µ and σ. The data set of N = 5
points had mean ¯x = 1.0 and
S = (x − ¯x) 2 = 1.0.