Chapter 13. Some Bayesian Approaches to Mixed Models

13.1

Introduction and Background

497

13.2

P-Values and Some Alternatives

499

13.3

Bayes Factors and Posterior Probabilities of Null Hypotheses

502

13.4

Example: Teaching Methods

507

13.5

Generating a Sample from the Posterior Distribution with the PRIOR Statement

509

13.6

Example: Beetle Fecundity

511

13.7

Summary

524

Introduction and Background

Most readers are likely aware of the strong resurgence of Bayesian methods over the past two decades due largely to the development and availability of efficient algorithms for generating samples from Bayesian posterior probability distributions, such as Markov Chain Monte Carlo (Gelfand et al. 1990, Tierney 1994, Robert 1994). Computations are now less of a critical difficulty ...

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