Dear BUGS listers & users,
I'm trying to fit a time-series model to yearly partridge densities in
an area in order to estimate density-dependence in population counts,
but I have problems with the WinBUGS script. I have information on the
sampling variability of each count, so I want to implement this
information within a state-space modeling scheme. The script I wrote is:
model{
for (j in 1:(n-1))
{
N[j+1] ~ dnorm(NExp[j+1], tau[j+1])
NExp[j+1] <- NExp[j] + (alpha + beta*NExp[j])*t[j]
t[j] <- year[j+1]-year[j]
}
alpha ~ dnorm(0,100)
beta ~ dnorm(0,100)
NExp[1] ~ dnorm(0, 0.001) I(0,)
}
list(n=28,
N =c(9.0494, 9.2762, 8.3308, 6.1738, 7.5562, 9.4902, 8.9029, 10.1562,
8.6708, 9.4329, 8.9079, 9.6969, 9.5282, 9.0537, 10.3862, 7.4413, 8.4357,
7.3265, 7.6087, 10.1140, 7.9270, 8.3854, 8.1562, 8.4044, 8.5383, 9.4498,
9.0336, 10.9816),
tau=c(6.3539, 7.4252, 6.0958, 4.4189, 5.9650, 8.0612, 6.6630,
7.4817, 6.7709, 7.5850, 7.2354, 6.6473, 7.1292, 6.1875, 6.9441,
5.4773, 6.8679, 6.0092, 5.5513, 8.5486, 6.0174, 6.4754, 4.8438,
5.7396, 6.4779, 7.2302, 6.5577, 8.6597),
year=c(1978, 1979, 1980, 1981, 1982, 1983, 1984, 1985, 1986, 1987, 1988,
1989, 1990, 1991, 1992, 1993, 1994, 1995, 1996, 1997, 1998, 1999, 2000,
2001, 2002, 2003, 2004, 2005))
NOTE: The basic process model I have in mind is a nonlinear
density-dependent growth model:
State process eqn. --> N[t+1]=N[t]+(alpha+beta*N[t]+epsilon)
were N(t+1) is population density, beta is the density-dependent
parameter to be estimated, and epsilon is process error
The observation model is:
Obs. process eqn. --> NExp[t+1]=N[t+1]+tau
were NExp[t+1] is the expected population density and tau is observation
error
N in data is population size, tau is sampling error.
I tried to specify a flat prior for alpha, and beta, dnorm(0, 100). I
have also tried to make NExp[j+1] dependent on NExp[j] and not on N[j].
I guess this is the main step in state-space modelling, is this OK? The
model is syntactically correct, but it hangs during the update. How can
I introduce further time lags in the model?
Thank you very much in advance
Pablo
--
Pablo Almaraz García
Estación Biológica de Doñana (CSIC)
Pabellón del Perú, Avda. Mª Luísa s/n
E-41013, Sevilla
SPAIN
E-mail: [log in to unmask]
webpage: http://www.almaraz.org
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