Description Usage Arguments Details Value Note Author(s) References See Also
View source: R/etas.starting.R
etas.starting
is a simple function to give starting values of the 8 ETAS parameters for the function etasclass
.
It gives only rough approximation, based on some assumptions, intended to give only the order of magnitude of each parameter (but should be better than nothing).
Returns a list with 8 starting values. With this betaversion user must give manually the output of this function in the input of etasclass
1 2 3 4 5 6 7 8 9  etas.starting(cat.orig,
m0=2.5,
p.start=1,
a.start=1.5,
gamma.start=0.5,
q.start=2,
longlat.to.km=TRUE,
sectoday=TRUE
)

cat.orig 
An earthquake catalog, possibly an object of class 
m0 
Threshold magnitude (only events with a magnitude at least 
p.start 
Parameter 4 of the ETAS model; the exponent of the Omori law for temporal decay rate of aftershocks; see details. Default value = 1.0. 
a.start 
Parameter 5 (α) of the ETAS model; efficiency of an event of given magnitude in generating aftershocks; see details. Default value = 1.5. 
gamma.start 
Parameter 6 (γ) of the ETAS model; together with 
q.start 
Parameter 8 of the ETAS model; parameter related to the spatial influence of the mainshock; see details. Default value = 2. 
sectoday 
if 
longlat.to.km 
if 
It is a betaversion of a very crude method to give
starting values for the eight parameters of an ETAS (Epidemic type aftershock sequences) model
for the description of the seismicity of a spacetime region.
These starting values can be used as input for the function etasclass
sectoday
and longlat.to.km
flags must the same that will be used in etasclass
.
In this first attempt to give starting values for the ETAS model, many approximations are used
It gives only rough approximation, based on some assumptions, intended to give only the order of magnitude of each parameter (but it should be better than nothing). It
returns a list with 8 starting values. With this betaversion user must give manually the output of this function in the input of etasclass
.
The values of p.start
, a.start
, gamma.start
and q.start
must be however given by the user (we did not find anything reasonable). Default choices for p
and q
(p.start=1
, q.start=2
) are strongly reccomended.
c
and d
are estimated from the emprical distributions of time differences and space distances, respectively.
mu
and k0
are then estimated from the starting valus the other six parameters, solving the two ML equations, that is derivatives of the whole likelihood with respect to mu
and k0
equated to zero.
In the computation of the likelihood an approximation for the integral of the intensity function is used (quoted also in
Schoenberg (2013)).
returns a list:
mu.start 
guess value for 
k0.start 
guess value for 
c.start 
guess value for 
p.start 
guess value for 
a.start 
guess value for 
gamma.start 
guess value for 
d.start 
guess value for 
q.start 
guess value for 
longlat.to.km 

sectoday 

The optimization algorithm used in etasclass
depends on the choice of initial values. Some default guess choice is performed in the present betaversion of the function etas.starting
. If convergence problem are experienced, a useful strategy can be to start with an high magnitude threshold value m0 (that is, with a smaller catalog with bigger earthquakes), and then using this first output as starting guess for a running with a lower magnitude threshold value m0.
In this trial executions avoid declustering (declustering=FALSE
) or at least use a small value of ndeclust
; small values of iterlim
and ntheta
can speed first executions.
Quicker executions are obtained using smaller values of iterlim
and ntheta
in the input.
Also a first execution with is.backconstant = TRUE
, to fit a first approximation model with constant background, can be useful.
Some other useful information can be obtained estimating a pure time process, that can give a good guess at least for some parameters, like mu, k0, a, c, p.
Input times are expected in days, and so final intensities are expected number of events per day. If input values are in seconds, then set sectoday=TRUE
Marcello Chiodi, Giada Adelfio
Schoenberg, F. P. (2013).Facilitated Estimation of ETAS. Bulletin of the Seismological Society of America, Vol. 103, No. 1, pp. 601605, February 2013, doi: 10.1785/0120120146
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