BPSpriorElicit {BayHaz}R Documentation

Function to Set Hyperparameters of BPS Priors

Description

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.

Usage

BPSpriorElicit(r0 = 1, H = 1, T00 = 1, ord = 4, G = 30, c = 0.9)

Arguments

r0 prior mean hazard rate (r_0)
H corresponding coefficient of variation
T00 time-horizon of interest (T_infty)
ord spline order (k)
G number of internal spline knots
c correlation coefficient between two consecutive spline weights

Details

A first order autoregressive BPS prior hazard rate is defined, for 0<t<T_infty, by

rho(t)=exp{sum_{j=1}^{G+k-2} eta_j B_j(t)}

where:

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 rho(t) is approximately equal to r0, for 0<t<T_infty, and its standard deviation to Hr_0.

Value

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

See Also

BayHaz-package, BPSpriorSample, BPSpostSample

Examples

# 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)

[Package BayHaz version 0.1-3 Index]