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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 non-frequentist. Examples will be given ranging from the location-scale problem to non-parametric regression and image analysis.

This talk is part of the Statistics series.

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