Statistical Methods

author: Paul Taylor, School of Mathematics, University of Manchester
published: Feb. 25, 2007,   recorded: June 2005,   views: 10564

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These two sessions give an introduction to classical statistics.

The first talk is a brief coverage of some basic statistical theory that I feel might be useful during the week. The topics included are: probability, likelihood inference, Bayesian inference and the concept of the bias variance tradeoff.

The second talk covers two main areas of statistics, namely linear modelling and exploratory multivariate analysis. Linear modelling has an elaborate set of procedures for determining which of the potential inputs should be included in a model for predicting an output. The inputs can be of any data type (categorical or numerical), as can the output to some extent. This sort of modelling has been used successfully for many years on what would be considered quite small sets of data. Some linear models are now being used on much larger problems, for example, in the construction of scorecards for deciding whether to approve somebody’s application for a credit card. This is the primary type of statistical model that would be used in scientific research. Exploratory multivariate analysis is a collection of techniques that are all based on the same sort of mathematical background (vectors/matrix algebra). They are also all intended to investigate the structure of observations that are vectors. Some of these techniques are being used on a massive scale in business; for example, hierarchical cluster analysis is used to build (offline) classifications of all the postal codes (each code represents about 16 houses) in a system such as Mosaic which is then used for targeting of marketing. The specific techniques covered are: principal components analysis; correspondence analysis; scaling; cluster analysis.

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