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T2.

3.7 Results

In this section we present analysis and results by applying the proposed method to
the phage display data described in section 3.3.

The parameter values in our proposed priors are elicited by consulting with the
investigators. The values of the hyper-parameters are the same as the ones used in
the simulation study. The parameter μ_i is interpreted as the expected counts if there
were no enrichment of the library of tripeptides at every stage and this is the case
for the first stage. We assume that most of the phage counts are small in the initial
state. Therefore, we set the expected value for the first stage counts μ_i to 0.1 and its
variance to 0.03. We do not assume any knowledge of the means increment between
the first and the second stage (in terms of β_i) and between the first and the third
stage (in terms of δ_i). We center these values around 6 allowing for a large variance
equal to 180.

We obtained a Monte Carlo posterior sample of size M = 5,000 storing the values
of the imputed parameters every ten iterations after a burn-in of 10,000 iterations.
Analogous to the simulation study, we performed convergence assessment for the
proposed parameter values to ensure that the MCMC algorithm converged well. We
found that the Markov chains mixed very well and converges rapidly.

Table 3.1 shows the 30 pairs with highest values of m_i, i.e the pairs chosen accord-
ing to the optimal rule (3.35) with a threshold value of seven. Figure 3.5 depicts these
pairs. We notice that there are some pairs, such as, the tripeptide ARF in the tissue
fat, that present a small posterior probability of increasing means, ρ_l, that would not
be selected according to the decision rule (3.31) but that are selected when using the
decision rule (3.35).

Using the optimal rule (3.35), with a threshold value of one, 219 tripeptide-tissue
pairs are selected. Figure 3.6 highlights these pairs. This criterion selects the pairs
clearly having high increasing counts across the three stages. Over some pairs with
nondecreasing counts, in agreement with its related utility function (3.34), the cri-

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