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In this lecture, we provide a
quick introduction into the

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conceptual framework of
classical statistics.

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We use the words "classical" to
make the distinction from

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the Bayesian framework that
we have been using so far.

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Recall that in the Bayesian
framework, unknown quantities

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are viewed as random variables
that have a certain prior

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distribution.

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In contrast, in the classical
setting an unknown quantity is

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viewed as a non-random constant
that just happens to

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be unknown.

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We can still carry out
estimation without assuming a

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prior for the unknown
quantity.

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For example, if the unknown
theta is the mean of a certain

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distribution, we can generate
many samples from that

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distribution and form
the sample mean.

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The weak law of large numbers
then tells us that this

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estimate will approach in the
limit as n increases the true

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value of theta.

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After going through this
argument, we will then take

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the occasion to introduce some
terminology that is often used

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in connection with classical
estimation methods.

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Now, the sample mean provides
us a point estimate for the

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unknown theta, but does not
tell us how accurate that

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estimate is.

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To give a sense of the
accuracy involved, we

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introduce the concept of a
confidence interval, which is

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an interval that has high
probability of containing the

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true theta.

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In general, it is a common
practice to report not just

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estimates, but also confidence
intervals.

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But as we will discuss, one
has to be careful in

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interpreting what exactly a
confidence interval tells us.

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We will see that we can easily
calculate confidence intervals

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using the central
limit theorem.

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And we will discuss in some
detail some extra steps that

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need to be taken if we do not
know the variance of the

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random variables involved.

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We will then continue in the
direction of greater

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generality.

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We will see that by repeated use
of various sample means,

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we can also estimate more
complicated quantities, such

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as, for example, the correlation
coefficient

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between two random variables.

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We will conclude by introducing
a general

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estimation methodology, the
so-called maximum likelihood

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estimation method.

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This is a method that applies
always, even when the unknown

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parameter of interest cannot
be interpreted as an

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expectation.

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It is a universally-applicable
method.

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And fortunately, has some very
desirable properties.