CPPpriorElicit {BayHaz} | R Documentation |
A function to set the hyperparameters of a CPP prior distribution, following the procedure described in La Rocca (2005).
CPPpriorElicit(r0 = 1, H = 1, T00 = 1, M00 = 1, extra = 0)
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) |
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).
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) |
As the default value of F
is computed a priori, additional jumps may be needed a posteriori.
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.
BayHaz-package
, CPPpriorSample
, CPPpostSample
# 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)