STATISTICAL INFERENCE AND CRITICISM

Inference and criticism are complementary facets of statistical analysis. Both are rooted in probability theory, but they address different questions about a model. 

Inference deals with the estimation of the parameters 0 of a postulated model from given data y. A natural way of doing this is to analyze the posterior density function p 6 y), constructed from the data and the postulated model according to Bayes theorem as described in Chapters 5-7. This approach includes the well-known method of least squares, as well as more general methods to be described in Chapter 7 and Appendix C. 

Criticism seeks to determine if a fitted model is faulty. This is done by examining the residuals (departures of the data from the fitted model) for any evidence of unusual or systematic errors. Sampling theory and diagnostic plots of the residuals are the natural tools for statistical criticism their use is demonstrated in Chapters 6 and 7 and in Appendix C. 

This view of the complementary roles of Bayesian inference and sampling theory is drawn from a landmark paper by Box (1980) and is followed consistently in this book. The controversy between Bayesians and sample theorists remains a lively one, but is becoming reconciled through the growing recognition that both approaches are useful and necessary. 

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