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src/content/lessons/maximum_likelihood.mdx

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@@ -24,10 +24,9 @@ The main idea of maximum likelihood is the following:
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- for each parameter $\theta$, one evaluates the density $p( \cdot | \theta)$ on the data points $x_1, \dots, x_n$: $p(x_1, \dots, x_n | \theta)$
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- then one chose the parameter $\theta$ that maximizes the likelihood of the observed data $p(x_1, \dots, x_n | \theta)$.
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<T block v='cal(L)^"ML" (theta) := log p(x_1, dots, x_n | theta)'/>
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<T block v=' := log p(x_1 | theta) times dots times p(x_n | theta) '/>
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<T block v=' := sum_(i=1)^n log p(x_i | theta) '/>
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<T block v='cal(L)^"ML" (theta)
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& := log p(x_1, dots, x_n | theta) \
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& = log p(x_1 | theta) times dots times p(x_n | theta) \
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& := sum_(i=1)^n log p(x_i | theta) '/>
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#### Examples

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