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Instead of trying
to find the best single setting of the
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parameters (as
in ML or MAP) compute the full posterior
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distribution over
parameter settings
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This
is extremely computationally intensive for all but
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the
simplest models (its
feasible for a biased coin).
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To make
predictions, let each different setting of the
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parameters make
its own prediction and then combine
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all these
predictions by weighting each of them by the
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posterior
probability of that setting of the parameters.
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This
is also computationally intensive.
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The full
Bayesian approach allows us to use complicated
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models even when
we do not have much data
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