# Chapter 17 Statistical Intervals for Bayesian Hierarchical Models

## Objectives and Overview

This chapter extends the introductory discussion of Bayesian statistical models presented in Chapters 15 and 16, and shows how to compute statistical intervals for more complicated statistical models and/or data structures. It provides an introduction to the analysis of hierarchical (or multilevel) statistical models using Bayesian analysis—to be referred to as “Bayesian hierarchical models” for short. We describe basic concepts underlying such analyses and illustrate their use in several different applications. The following topics are discussed:

• The basic ideas for modeling data from multilevel (hierarchical) studies (Section 17.1).
• Hierarchical models for data that can be described by a normal distribution (Section 17.2).
• Hierarchical models for data that can be described by a binomial distribution (Section 17.3).
• Hierarchical models for data that can be described by a Poisson distribution (Section 17.4).
• The analysis of data when repeated measurement are taken on a sample of units over time, which can also be viewed as a hierarchical model (Section 17.5).

As indicated in Section 15.1.1 and illustrated by various examples in Chapters 15 and 16, one important motivation for using Bayesian methods is to incorporate prior information into a data analysis/modeling problem, especially to supplement limited data. In this chapter, however, the primary motivation is that Bayesian methods ...

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