Reference Priors {#sub3sec4}
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Despite its success in the one-parameter context, Jeffreys’ non-informative prior methodology often runs into serious difficulties in multiparameter problems [@DattaGhosh1996]. The prior distribution may be difficult to derive and too complex to be easily interpretable. This is often the case when several nuisance parameters are present. For our problem, Jeffreys’ prior is difficult to interpret given that it depends on the ratio of sample sizes $m_{+1}$ and $m_{+0}$. In this context, the reference prior may be more preferred [@Bernardo1979; @BergerBernardo1989], loosely defined as vague priors with the least amount of information. Here, we divide the vector of parameters into two sets: parameters of interest and nuisance parameters. Then, we consider the parameters sequentially in the process of deriving a reference prior. @BergerBernardo1992a [@BergerBernardo1992b; @BergerBernardo1992c] took this idea to another level by suggesting to split the parameter vector into multiple groups according to their orders of inferential importance. The two authors provided a general algorithm for the construction of reference priors. Hence, reference priors are not uniquely defined. We derive the reference prior for the parameters $\gamma$, $U$, and $V$, leading to an induced reference prior for $\gamma$, $\lambda_0$, and $\lambda_1$.

We start with the two group 