STATISTICS COLLOQUIUM

THURSDAY, November 12^th, 2009 at 4.10pm, MSB 1147 (Colloquium Room)

Refreshments: 3.30pm, MSB 4110 (Statistics Lounge)

Speaker:            P.L. Davies (University of Duisburg-Essen, Germany)

Title:                Approximating Data

Abstract:             A model is regarded as an adequate approximation to a data set if `typical' data generated under the model `looks like' the real data. The word `typical' is made precise by specifying a real number a, 0 < a < 1, which determines what percentage of the data sets generated under the model, are to be regarded as typical. The words `look like' must be operationalized (in practice often in the form of a computer program) so that for any model and any data set it is possible to decide whether the model is an adequate approximation to the data. The precise nature of this will depend on the problem at hand; there is no general principle which can be used. Typically there will be many adequate models and interest will center on certain simplest ones where simplicity can be defined in terms of shape (e.g. the minimum number of local extreme values) or smoothness (minimum total variation of a derivative) or the absence of `free lunches' (minimum Fisher information). The ideas and the applications will be illustrated by several examples, amongst others, from the area of nonparametric regression.

Reference:       Davies,~P.~L. (2008) Approximating data (with discussion), Journal of the Korean Statistical Society, 37, 191-240.

Please see the attachment below for slides of this talk.