20 In praise of Bayes

It is hard for us today to capture the intensity of the intellectual struggles that past pioneers in any field of knowledge engaged in as, with insight, creativity and sheer hard work, they laid the foundations of that field. However, we can improve our understanding of these struggles if we have some historical knowledge. That is why there are vignettes from the history of statistics in many places in this book.

CHAPTER 22, in particular, gives a broad perspective over some 400 years on the development of statistical inference. In the main, this is a history of frequentism in statistics.

Frequentism is a conceptual framework for statistical theory which takes its name from one of its fundamental axioms – that probability is best defined objectively as an empirical relative frequency. Unfortunately for any hope of a tidy intellectual evolution of the field, some 18th century statistical thinkers saw scope for an alternative framework for statistical theory, using as a fundamental axiom the subjective definition of probability. This conceptual framework has become known as Bayesianism, as we explain below.

Today, frequentism and Bayesianism are thriving as rival paradigms, both for designing theoretical techniques and for interpreting the results of applying those techniques to data. In this chapter, we look at the origins of Bayesianism and show why Bayesian inference is sometimes (its practitioners would say ‘always’) more appealing than the frequentist ...

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