BPSpriorElicit: Function to Set Hyperparameters of BPS Priors
In BayHaz: R Functions for Bayesian Hazard Rate Estimation

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

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# 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)