Introduction to Bayesian Statistics (Bolstad/Bayesian Statistics) || Comparing Bayesian and Frequentist Inferences for Proportion

✍ Scribed by Bolstad, William M.

• Publisher: John Wiley & Sons, Inc.
• Year: 2005
• Tongue: English
• Weight: 183 KB
• Edition: 1
• Category: Article
• ISBN: 0471270202
• DOI: 10.1002/047172212x.ch9

✦ Synopsis

Comparing Bayesian and Frequentist Inferences for Proportion

The posterior distribution of the parameter given the data gives the complete inference from the Bayesian point of view. It summarizes our belief about the parameter after we have analyzed the data. However, from the frequentist point of view there are several different types of inference that can be made about the parameter. These include point estimation, interval estimation, and hypothesis testing. These frequentist inferences about the parameter require probabilities calculated from the sampling distribution of the data, given the fixed but unknown parameter. These probabilities are based on all possible random samples that could have occurred. These probabilities are not conditional on the actual sample that did occur!

In this chapter we will see how we can do these types of inferences using the Bayesian viewpoint. These Bayesian inferences will use probabilities calculated from the posterior distribution. That makes them conditional on the sample that actually did occur.

9.1 FREQUENTIST INTERPRETATION OF PROBABILITY AND PARAMETERS

Most statistical work is done using the frequentist paradigm. A random sample of observations is drawn from a distribution with an unknown parameter. The parameter is assumed to be a fixed but unknown constant. This doesn't allow any probability distribution to be associated with it. The only probability considered is the probability