In Chaps. 6 and 7, before making inferences about parameters of interest (e.g. before comparing treatments), we wrote a model containing ‘noise’ effects and effects of interest and we described which was the prior information of these effects, or in a frequentist context whether they were ‘fixed’ or ‘random’. We have assumed we know the right model without discussing whether there was a more appropriate model for our inferences. We can think that a better model could have been used to get better inferences. We can also think that we have underestimated our uncertainty, since we have some uncertainty about which is the best model for our inferences that we have not taken into account. The first problem is the goal of this chapter: how to choose the best model. The second problem has a difficult solution, since we cannot take into account all possible models to describe a natural phenomenon.
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- Bernardo JM (2005) Reference analysis. In: Dey DK, Rao CR (eds) Handbook of statistics, vol 25. Elsevier, Amsterdam, pp 17–90Google Scholar
- Burnham KP, Anderson KR (2002) Model selection and multimodel inference. Springer, New YorkGoogle Scholar
- Edgeworth FY (1908) On the probable error of frequency constants. J R Stat Soc 71:381–397, 499–512, 651–678, Addendum in 1908, 72:81–90Google Scholar
- Hald A (1998) A history of mathematical statistics from 1750 to 1930. Wiley, New YorkGoogle Scholar
- Sober E (2016) Occam’s razor. Cambridge University Press, CambridgeGoogle Scholar
- Stove D (1982) Popper and after: four modern irrationalists. Pergamon, OxfordGoogle Scholar