2.7 Summary
The differences between the Bayesian and Frequentist inferential approaches are philosophical, particularly with regard to the role of probability; pedagogical, especially in relation to the use of inference for decision-making; and methodological, due to differences in their mathematical and computational frameworks. Although, at the methodological level, the debate has become considerably muted —except for certain aspects of inference— there is widespread recognition that each approach has much to contribute to statistical practice (Good (1992), M. J. Bayarri and Berger (2004), R. Kass (2011)). As Bradley Efron stated, “Computer-age statistical inference at its most successful combines elements of the two philosophies” (Bradley Efron and Hastie (2016)).