Modeling Measurement and Count Data
DOI link for Modeling Measurement and Count Data
Modeling Measurement and Count Data book
This chapter discusses different ways to specify a prior distribution for a mean parameter. One attractive discrete approach for expressing this prior opinion for a proportion has two steps. First one constructs a list of possible values of the mean parameter, and then one assigns probabilities to the possible values to reflect one’s belief. The chapter describes the use of a continuous prior to represent one’s belief for the mean parameter. This is a more realistic approach for constructing a prior since one typically views the mean as a real-valued parameter. The chapter discusses how to construct a prior distribution that matches one’s prior belief, how to extract information from the data by the likelihood function, and how to update one’s opinion in the posterior, combining the prior and data information in a natural way. It also introduces a popular one-parameter model for counts, the Poisson distribution, and its conjugate gamma distribution for representing prior opinion.