Seminar: Model Assumptions and Truth in Statistics

SpeakerChristian Hennig
AffiliationUniversity College London, Statistics
DateThursday, 07 May 2015
Time16:00 - 17:00
LocationRoom 102, 1-19 Torrington Place, Department of Statistical Science
Event seriesStatistical Science Seminars
Description

The way statistics is usually taught and statistical analyses are usually presented can easily seem mysterious. For example, statisticians use methods that assume the data to be normally distributed, and they insist that this assumption needs to be tested for the analysis to be justified, but the same statisticians would also state on another day that they don't believe any such model assumption to be true anyway. Does it make sense to test an assumption that we don't believe to hold regardless of the outcome of the test, and does it make sense to build our methodology on such assumptions?

As a statistician with a long-standing interest in philosophy I built my own way of understanding the reasons for what statisticians do, and that and why these reasons sometimes work well, but sometimes are less convincing. This understanding is influenced by constructivist philosophy and by a framework for relating mathematical models to the reality that we observe and that we deal with in science. That's what this presentation is about.

I will discuss how Frequentist and Bayesian statistics can be understood in terms of what way of thinking about the modelled phenomena they imply, and in what way what is misleadingly called "test of the model assumptions" can inform statistical analyses. This involves taking the unbridgeable gap between models and the modelled reality seriously, and explaining the use of models without referring to them as being supposedly "true". I will also discuss the idea of "approximating" reality by statistical models (Davies, 2014), and mention some practical implications for evaluating the quality of statistical methods in my core statistical research area, which is Cluster Analysis (finding groups in data).

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