BayHaz (version 0.1-3)

BPSpriorElicit: 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

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

Details

A first order autoregressive BPS prior hazard rate is defined, for $0

$\eta_j$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$T_\infty$(seesplineDesignfor 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 $\rho(t)$ is approximately equal to $r0$, for $0

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)