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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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