Approximating Data
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If you have a question about this talk, please contact Richard Samworth.
The talk will describe an approach to much of statistics in which
probability models are consistently treated as approximations to the data. It
is not assumed that the data are distributed as in the model, nor does
one behave as if this were true whilst being conscious of the fact
that it is not. A model P is regarded as an adequate approximation to
the data x of size n if ‘typical’ samples X(P) of size n simulated under the
data ‘look like’ x. The words ‘typical’ and ‘looks like’ must be given
precise meanings which will depend on the problem. The approach has
several consequences some of which may be unexpected: there are no
‘true but unknown’ parameter values and the interpretation of
confidence or approximation intervals is nonfrequentist. Examples will be
given ranging from the locationscale problem to nonparametric
regression and image analysis.
This talk is part of the Statistics series.
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