By Jon Wakefield

*Bayesian and Frequentist Regression Methods* provides a latest account of either Bayesian and frequentist equipment of regression research. Many texts disguise one or the opposite of the ways, yet this can be the main accomplished mixture of Bayesian and frequentist tools that exists in a single place.

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**Example text**

As discussed in Sect. 2, model formulation should begin with a model that we would like to fit, before proceeding to examine its mathematical properties. As we will see, exponential family models can provide robust inference, in the sense of performing well even if certain aspects of the assumed model are wrong, but to only consider these models is unnecessarily restrictive. We now discuss how estimators may be compared in general circumstances asymptotically, that is, as n → ∞. There are two hypothetical situations that are being considered here.

The level of belief in this model will clearly be context specific, and in many situations, there will be insufficient information available to confidently specify all components of the model. Depending on the confidence in the likelihood, which in turn depends on the sample size (since large n allows more reliable examination of the assumptions of the model), the likelihood may be effectively viewed as approximately “correct,” in which case inference proceeds as if the true model were known. Alternatively the likelihood may be seen as an initial working model from which an estimating function is derived; the properties of the subsequent estimator may then be determined under a more general model.

Distinguishing Features. Poisson regression models for independent data, and extensions to allow for excess-Poisson variation, are described in Chap. 6. Such models are explicitly designed for nonnegative response variables. Accounting for residual spatial dependence is considered in Chap. 9. 4 Pharmacokinetic Data Pharmacokinetics is the study of the time course of a drug and its metabolites after introduction into the body. , orally or via an injection) at a known time. Subsequently, blood samples are taken, and the concentration of the drug is measured.