Description Usage Arguments Details Value See Also Examples
A function to set the hyperparameters of a first order autoregressive BPS prior distribution, approximately assigning constant prior mean hazard rate and corresponding coefficient of variation.
1 | BPSpriorElicit(r0 = 1, H = 1, T00 = 1, ord = 4, G = 30, c = 0.9)
|
r0 |
prior mean hazard rate (r_0) |
H |
corresponding coefficient of variation |
T00 |
time-horizon of interest (T_∞) |
ord |
spline order (k) |
G |
number of internal spline knots |
c |
correlation coefficient between two consecutive spline weights |
A first order autoregressive BPS prior hazard rate is defined, for 0<t<T_∞, by
ρ(t)=\exp\{∑_{j=1}^{G+k-2} η_j B_j(t)\}
where:
η_j is the j-th element of a normally distributed vector of spline weights (see below for details)
B_j(t) is the j-th B-spline basis function of order k, evaluated at t,
defined on a grid of G+2k-2 equispaced knots with first internal knot at 0
and last internal knot at T_∞ (see splineDesign
for details)
The spline weights form a stationary AR(1) process with mean m, variance w and lag-one autocorrelation c. The elicitation procedure takes w = H^2 and m = \log r_0 - 0.5 * w, based on the mean and variance formulas for the log-normal distribution. As B-spline basis functions form a partition of unity within internal nodes, the mean of ρ(t) is approximately equal to r0, for 0<t<T_∞, and its standard deviation to Hr_0.
A list with nine components:
r0 |
prior mean hazard rate (copy of the input argument) |
H |
corresponding coefficient of variation (copy of the input argument) |
T00 |
time-horizon of interest (copy of the input argument) |
ord |
spline order (copy of the input argument) |
G |
number of internal spline knots (copy of the input argument) |
c |
correlation coefficient between two consecutive spline weights (copy of the input argument) |
knots |
full grid of spline knots |
m |
mean of spline coefficients |
w |
variance of spline coefficients |
BayHaz-package
, BPSpriorSample
, BPSpostSample
1 2 3 | # ten events per century with unit coefficient of variation and fifty year time horizon
# cubic splines with minimal number of knots and strongly correlated spline weights
hypars<-BPSpriorElicit(r0 = 0.1, H = 1, T00 = 50, ord = 4, G = 3, c = 0.9)
|
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