Bayes' Theorem for Distributions
Svein Olav Nyberg · 2018
In this chapter, Bayes' theorem is used to find a new probability distribution for the sample. It deals with a discrete prior and a continuous prior to find this new distribution. Next, the chapter discusses how to calculate the probability distributions of all possible observations. It then describes the general rule for updating a probability distribution. One make further updates by setting the new prior equal to the old posterior distribution. For that, he/she needs to extend the table for calculating the next observation with a column for the posterior distribution. The chapter explains how to select a prior. Sensitivity to prior is the first concern in choosing a prior. For big data sets, the prior must be very informative if it is to make much of a difference, and such priors usually arise only as the posterior probability distribution from previous investigations.