viii
3.1 Base measure Eb=Glα(9,2), posterior base measure Fi := E(F ∣ xn), em-
pirical cdf and set of simulated measures sampled from the posterior distri-
bution of the DP(α = 5,77b) when a sample xn: 1,2,2,3,3 and 3 of this DP
was observed................................. 44
3.2 Histogram of the house prices in Boston. The continuous line is the non-
parametric estimation of the corresponding density function using the MDP
model in (3.25) .............................. 56
3.3 Observed sequence of tripeptide-tissue pair counts across the three stages.
Each line represents the three observed counts of a pair. The three pan-
els depicts the pairs with: (a) non decreasing, (b) oscillating and (c) non
increasing counts.............................. 59
3.4 Histograms of a simulated sample of future observations of β and δ. They
estimate the true probability density function (continuous line) of the dis-
tribution that generated the data ..................... 71
3.5 Thirty pairs with highest estimated values of rr⅛ in (3.36). Lower section
presents counts for the three stages: circle, triangle and cross. The mid-
dle section shows the value of mi. The upper part depicts the posterior
probability of increasing means across the three stages, pi......... 74
3.6 Respectively, (a) and (b) nondecreasing and oscillating observed tripeptide-
tissue pair counts across the three stages. In red the 219 selected pairs using
the optimal rule (3.35) with a threshold value of 1............. 75
3.7 Histograms of simulated samples of the final distribution of the parameters
βi and <5j for three specific pairs....................... 76