The name is absent

99

model.

4.5 Results

We implemented inference for the data described in Section 4.2 using the proposed
non-exchangeable partition model 4.1 with 7 = 1. The parameter a of the Dirichlet
process associated with the probability in the space of partitions of the space of indices
was assumed to be G^rα(5,0.5) distributed.

Saving every 10^tft iteration after a 10,000 iteration burn-in, a Monte Carlo posterior
sample of size 10,000 was saved to estimate the success rates. The Markov chain mixed
well.Both the central 95% credible intervals and the 5% percentile of the success
rate Pi for each sarcoma subtype in the study are shown in Figure 4.5. Only for
Angiosarcoma, Synovial and MFH we find posterior probabilities greater 95% that p_i
is greater than 0.1.

4.6 Discussion

We proposed an approach to borrow strength across non-exchangeable subpopula-
tions. The usual approach to borrow strength across subpopulations is through hier-
archical models, perhaps one of the most successful Bayesian approaches in biomedical
data analysis. In a hierarchical model, the estimation of any subpopulation-specific
effect borrows the same amount of strength from all observation in other subpop-
ulations. In a partially exchangeable hierarchical regression model inference bor-
rows strength across all subpopulations that are grouped together in some fixed a
priori grouping by covariates. In contrast, the proposed model introduces the non-
exchangeability only stochastically, with random partitions, through the prior distri-
bution and the estimation of subpopulation-specific effects p_i borrows more strength
from the subset of observations, that according to our prior beliefs, are exchangeable

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