Description Usage Arguments Details Value Note References See Also Examples
A function to set the hyperparameters of a CPP prior distribution, following the procedure described in La Rocca (2005).
1  CPPpriorElicit(r0 = 1, H = 1, T00 = 1, M00 = 1, extra = 0)

r0 
prior mean hazard rate (r_0) 
H 
corresponding coefficient of variation 
T00 
timehorizon of interest (T_∞) 
M00 
number of extremes within the timehorizon in a "typical" hazard rate trajectory (M_∞) 
extra 
number of additional CPP jumps (compared with default) 
A CPP prior hazard rate is defined, for 0<t<T_∞, by
ρ(t)=ξ_0 k_0(t)+∑_{j=1}^{F} ξ_j k(tσ_j)
where:
σ_j is the time of the jth jump of a CPP process with gamma distributed jumpsizes
ξ_j is the jth jumpsize of the above process
k is a zeromean Gaussian density (kernel)
F is a positive integer such that (with high probability) σ_{F+1} is much larger than T_∞
ξ_0 is an independent random variable with the same distribution as ξ_j
k_0 is a suitable function such that the mean of rho(t) does not depend on t
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 jumpsizes. The kernel bandwidth choice is based on M_∞ (and T_∞).
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 
timehorizon of interest (copy of the input argument) 
M00 
number of extremes within the timehorizon in a "typical" hazard rate trajectory (copy of the input argument) 
a 
shape parameter of the jumpsize 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 jumpsize distribution 
F 
maximum number of jumps within the timehorizon (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. 3805, Department of Social, Cognitive and Quantitative Sciences, Reggio Emilia, Italy.
BayHazpackage
, CPPpriorSample
, CPPpostSample
1 2 3  # 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)

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