Some Aspects of Model Estimation and Model Criticism.
Technical summary rept.,
WISCONSIN UNIV-MADISON MATHEMATICS RESEARCH CENTER
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The recently advanced philosophy of model building is developed further. It is stressed how Bayesian inferences based on the posterior distribution of the model parameters are appropriate only after sampling theory inferences based on the predictive distribution of the data fail to discredit the model. An example involving the normal distribution is discussed in detail. Diagnostic checking functions are developed which can be applied in an intuitive sequential manner. Careful attention is also given to the nature of the predictive distribution for the extreme situation where information about the parameters is very precise or very vague. For the latter case, it is illustrated how the predictive distribution can simultaneously i reflect this vague information in an appropriate manner and ii allow for the checking of the adequacy of the basic distributional assumptions such as normality and independence. A particular problem in the interpretation of predictive distributions arises in situations involving a discrete data-generating distribution with vague prior knowledge about the parameters. This problem is explored in depth for the case of the binomial distribution. Author
- Statistics and Probability