This Chapter describes methods for assessing the hyperparameters for prior distributions used to quantify available prior knowledge regarding parameter values. When observed data arise from Binomial, Scalar Normal, Multivariate Normal, and Matrix Normal distributions as in this text, the prior distributions of the parameters of these distributions contain parameters themselves termed hyperparameters. These prior distributions are quite often the Scalar Beta, Scalar Normal, Multivariate Normal, Matrix Normal, Inverted Gamma, and Inverted Wishart distributions. The hyperparameters of these prior distributions need to be assessed so that the prior distribution can be identiﬁed. There are two ways the hyperparameters can be assessed, either in a pure subjective way which expresses expert knowledge and beliefs or by use of data from a previous similar experiment. Throughout this chapter, we will be in the predata acquisition stage of an

experiment. We will quantify available prior knowledge regarding values of parameters of the model which is speciﬁed with a likelihood. We will quantify how likely the values of the parameters in the likelihood are, prior to seeing any current data. This can be accomplished by using data from a previous similar experiment or by using subjective expert opinion in the form of a virtual set of data.