It is often the case that we need to do sample comparison: we have someone else's data to compare with ours; or someone else's model to compare with our data; or even our data to compare with our model. We need to make the comparison and to decide something. We are doing hypothesis testing – are our data consistent with a model, with somebody else's data? In searching for correlations as we were in Chapter 4, we were hypothesis testing; in the model fitting of Chapter 6 we are involved in data modelling and parameter estimation.

Classical methods of hypothesis testing may be either parametric or non-parametric, distribution-free as it is sometimes called. Bayesian methods necessarily involve a known distribution. We have described the concepts of Bayesian versus frequentist and parametric versus non-parametric in the introductory Chapters 1 and 2. Table 5.1 summarizes these apparent dichotomies and indicates appropriate usage.

That non-parametric Bayesian tests do not exist appears self-evident, as the key Bayesian feature is the probability of a particular model in the face of the data. However, it is not quite this clear-cut, and there has been consideration of non-parametric methods in a Bayesian context (Gull & Fielden 1986). If we understand the data so that we can model its collection process, then the Bayesian route beckons (see Chapter 2 and its examples).