CPPpriorElicit {BayHaz}R Documentation

Function to Set Hyperparameters of CPP Priors

Description

A function to set the hyperparameters of a CPP prior distribution, following the procedure described in La Rocca (2005).

Usage

CPPpriorElicit(r0 = 1, H = 1, T00 = 1, M00 = 1, extra = 0)

Arguments

r0 prior mean hazard rate (r_0)
H corresponding coefficient of variation
T00 time-horizon of interest (T_infty)
M00 number of extremes within the time-horizon in a "typical" hazard rate trajectory (M_infty)
extra number of additional CPP jumps (compared with default)

Details

A CPP prior hazard rate is defined, for 0<t<T_infty, by

rho(t)=xi_0 k_0(t)+sum_{j=1}^{F} xi_j k(t-σ_j)

where:

The elicitation procedure makes the mean of rho(t) identically equal to r_0 and its standard deviation approximately equal to Hr_0. An exponential distribution is selected for the jump-sizes. The kernel bandwidth choice is based on M_infty (and T_infty).

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)
M00 number of extremes within the time-horizon in a "typical" hazard rate trajectory (copy of the input argument)
a shape parameter of the jump-size distribution (always equal to 1)
sd standard deviation of the Gaussian kernel (bandwidth)
q expected number of CPP jumps per time unit
b rate parameter of the jump-size distribution
F maximum number of jumps within the time-horizon (with high probability)

Note

As the default value of F is computed a priori, additional jumps may be needed a posteriori.

References

Luca La Rocca (2005). On Bayesian Nonparametric Estimation of Smooth Hazard Rates with a View to Seismic Hazard Assessment. Research Report n. 38-05, Department of Social, Cognitive and Quantitative Sciences, Reggio Emilia, Italy.

See Also

BayHaz-package, CPPpriorSample, CPPpostSample

Examples

# ten events per century with unit coefficient of variation
# fifty year time horizon with a couple of extremes in a "typical" trajectory
hypars<-CPPpriorElicit(r0 = 0.1, H = 1, T00 = 50, M00 = 2)

[Package BayHaz version 0.1-3 Index]