Biomedical Engineering Reference
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coecient function of one, that is, a random intercept, we specify the same
type of priors for both the logarithm of the baseline hazard function and the
covariate coecient functions. In the following, we use '(t) to denote either
log h 0 (t) or one component in (t) to discuss our prior specications. For ease
of notation, we drop the dependence of the hyperparameters on j used in
Section 7.2.5.
Following Wang et al. (2011a), we first assume that the number of jumps
J follows a discrete uniform distribution range from 1 to K. For a fixed J, the
jump times 0 < 1 < ::: < J = a K except the last one are randomly selected
from all points in grid Gf 1 ;:::; J g G. Given both J and the jump times,
we then assume a hierarchical AR prior (7.11) for f'( 1 );'( 1 );:::;'( K )g.
Specifically, we assume
'( 1 ) N(0;c 0 w 2 );
'( j ) j '( j1 ) N '( j1 );w 2 ; j = 2; 3;:::;J;
(7.12)
w 2 IG( 0 ; 0 );
where c 0 , 0 , and 0 are prespecified hyperparameters.
The dynamic prior for '(t) determines the posterior structure of the base-
line hazard function or the coecient functions, and controls the regulariza-
tion of these curves. This prior penalizes quadratic variation of the coecient
function to yield a smoother curve, borrowing strength from adjacent values
when sampling each piecewise constant function. The posterior inferences are
more robust to the specification of hyperparameters than those for the fully
time-varying coecients in Sinha et al. (1999). The change in the dimension of
model parameters for different values of J requires a reversible jump MCMC
algorithm (Green, 1995) to sample from the posterior distribution, which is
outlined in Section 7.3.
 
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