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

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

 `1` ```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_∞) `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_∞, 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.

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

`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) ```