The name is absent

39

in the unselected library in the second row. The two columns are A versus not A.
They carry out a test of independence in these two-by-two contingency tables, using
Fisher’s exact test. Finally, in a third step they consider a similar two-by-two table,
but now with the second row reporting counts for all tissues (after stage 3). Again, a
test for independence is carried out to test for preferential binding of A to tissue T.
A peptide A passing all three filters is reported as binding with high affinity to tissue
T.

Ji et al. (2007) proposed a Bayesian hierarchical model as a way of accounting
for correlation between measurements and reducing the number of parameters. They
used a False Discovery Rate (FDR) criterion (see, Newton, 2004) to report high-
binding peptides for a 3-stage phage display experiment with mouse data. Later,
in Section 3, we argue that this parametric hierarchical model is inappropriate for
the human data described below. Taking advantage of the large sample size of our
data set, we propose instead a semiparametric Bayesian model that avoids some of
the limitations of the fully parametric model described by Ji et al. Also, we propose
an alternative criterion to select high-binding peptides based on a decision theoretic
framework.

The main contributions of this paper is the use of a non-parametric prior to
avoid the limitations of specific parametric assumptions, and the use of a decision
theoretic framework to address the multiplicity issues arising in the selection of a list
of tripeptides-tissue pairs that are reported for significant affinity.

The remainder of this chapter is organized as follows. The proposed model is a
Dirichlet Process Mixture (DPM) model, Section 3.2 reviews the basic properties of
the Dirichlet Process and DPM models, describes the standard MCMC algorithm to
simulate posterior samples from this latter model and gives an example of an applica-
tion of DPM model in density estimation. Section 3.3 presents a detailed description
of the multistage human data. In section 3.4 We propose a Bayesian semi-parametric
mixture Poisson model and describe the Markov Chain Monte Carlo(MCMC) simula-

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