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Bayesian Data Analysis, Third Edition, 3rd Edition by Donald B. Rubin, Aki Vehtari, David B. Dunson, Hal S. Stern, John B. Carlin, Andrew Gelman

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Chapter 2

Single-parameter models

Our first detailed discussion of Bayesian inference is in the context of statistical models where only a single scalar parameter is to be estimated; that is, the estimand θ is one-dimensional. In this chapter, we consider four fundamental and widely used one-dimensional models—the binomial, normal, Poisson, and exponential—and at the same time introduce important concepts and computational methods for Bayesian data analysis.

2.1   Estimating a probability from binomial data

In the simple binomial model, the aim ...

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