192 CH A P T E R 9: Bernoulli Likelihood with Hierarchical Prior to estimate the bias in each coin. The prior beliefs about each parameter were assumed to be independent of each other, which meant that our prior belief about the bias in one coin had no influence about our prior belief regarding the bias in the other coin. This independence of the parameters meant that the formal specification of the prior belief about either coin's bias had no mention of the other bias. In this chapter, we explore situations in which there are two or more parame- ters that do have meaningful dependencies. For example, we may believe that the bias of a coin depends on the characteristics of the factory in which it was minted. We have prior beliefs about the parameter values of the mint, and we have prior beliefs about the dependence of the coin's bias on the minting parameters. Then we flip the coin a few times and observe how many times it comes up heads. The data affect our beliefs about the coin's bias. But, impor- tantly, the data also affect our beliefs about the dependence of the coin's bias on the minting parameters, and the data affect our belief about the minting parameters themselves. The parameters that directly affect the data are called just that: parameters.