MetaLandSim (version 2.0.0)

ifm.naive.MCMC: Estimate the naive design incidence function model

Description

Estimates the IFM assuming no false absences and omitting sites for particular years in which data were missing.

Usage

ifm.naive.MCMC(niter=1000,init,z.data, site.distance, site.area, sd.prop.e=0.2,
 sd.prop.x=0.5,sd.prop.y=10, sd.prop.b=0.2, sd.prop.alpha=5,nthin=1,print.by=100)

Value

e.chain

posterior sample of e

x.chain

posterior sampmle of x

y.chain

posterior sample of y

b.chain

posterior sample of b

alpha.chain

posterior sample of alpha

deviance.chain

posterior sample of -2*loglik

Arguments

niter

Number of iterations in the MCMC chain.

init

Named list with values to initialize the chain. E.g.:

init1=list(alpha=runif(1,1,30), b=runif(1,0,5),y=runif(1,0,20),

e=runif(1,0,1),x=runif(1,0,5)).

alpha: initial value for alpha in dispersal model; described as 1 / average dispersal distance

b: initial value for parameter b in colonization model

y: initial value for parameter y in colonization model

e: initial value for e in extinction model

x: initial value for x in extinction model

z.data

nsite x nyears matrix. If contains NAs, the corresponding parts are omitted from the likelihood (the missing data are not estimated).

site.distance

nsite x nsite matrix of distances between sites. The tuning parameters in the example are set for distances less than one, with max distance approximately 0.5.

site.area

Vector of length nsite with areas. The tuning parameters in the example are set for average area approximately equal to 1.

sd.prop.e

Standard deviation of the proposal distribution for parameter e.

sd.prop.x

Standard deviation of the proposal distribution for parameter x.

sd.prop.y

Standard deviation of the proposal distribution for parameter y.

sd.prop.b

Standard deviation of the proposal distribution for parameter b.

sd.prop.alpha

Standard deviation of the proposal distribution for parameter alpha.

nthin

If specified, keeps only every nthin^th sample from the MCMC chain. Use to save memory or when the chain is moving slowly.

print.by

Specifies how often to print the number of the current iteration.

Author

Benjamin Risk

References

Risk, B. B., De Valpine, P., Beissinger, S. R. (2011). A robust design formulation of the incidence function model of metapopulation dynamics applied to two species of rails. Ecology, 92(2), 462-474.

Examples

if (FALSE) {
data(simulatedifm)

library("coda")

myniter=5000
nsite=nrow(z.sim)
nyear=ncol(z.sim)
nthin=1
nburnin=1000
## NOTE! The notation used here corresponds to MetaLandSim and differs from Risk et al 2011
## Here
## e (in MetaLandSim) = mu
## x = chi
## y = gamma
## b = beta
## alpha = alpha
##
# Priors:
#         e: [0,1]
#         x: [0,5]
#         y^2: [0,400]
#         b: [0,5]
#         alpha: [1,30]

# NOTE: If posteriors are truncated at zero, then estimates are biased. Rescale
# distances (e.g., divide by 10,000) and/or areas so that parameters are larger.

# Here, we run two chains with random initial values:
init1=list(alpha=runif(1,1,30), b=runif(1,0,5),y=runif(1,0,20),e=runif(1,0,1),x=runif(1,0,5))

a = Sys.time()
inm1 <- ifm.naive.MCMC(niter=myniter,init=init1,z.data =
 z.sim,site.distance=sim.distance,site.area=sim.area,
  sd.prop.alpha=4,sd.prop.b=0.6,sd.prop.y=40,sd.prop.e=0.05,sd.prop.x=0.4,nthin=1,print.by=1000)
accept.calculate(inm1,model='naive')
Sys.time() - a

init2=list(alpha=runif(1,1,30), b=runif(1,0,5),y=runif(1,0,20),e=runif(1,0,1),x=runif(1,0,5))
inm2 <- ifm.naive.MCMC(niter=myniter,init=init2,z.data =
z.sim,site.distance=sim.distance,site.area=sim.area,
sd.prop.alpha=4,sd.prop.b=0.6,sd.prop.y=40,sd.prop.e=0.05,sd.prop.x=0.4,nthin=1,print.by=1000)
accept.calculate(inm2,model='naive')
Sys.time() - a

coda.create(inm1,"sim_inm1",par.list=list("e.chain","x.chain","alpha.chain",
"b.chain","y.chain"),niter=myniter,nthin=nthin)
coda.create(inm2,"sim_inm2",par.list=list("e.chain","x.chain","alpha.chain",
"b.chain","y.chain"),niter=myniter,nthin=nthin)
coda.sim.inm1=read.coda("sim_inm1.txt","sim_inm1_Index.txt")
coda.sim.inm2=read.coda("sim_inm2.txt","sim_inm2_Index.txt")
coda.sim.inm.list=mcmc.list(coda.sim.inm1,coda.sim.inm2)
sim.inm=combine.chains(inm1,inm2,nburnin=nburnin,nthin=1)
coda.create(sim.inm,"sim_inm",par.list=list("e.chain","x.chain","alpha.chain",
"b.chain","y.chain"),niter=(2*myniter-2*nburnin),nthin=nthin)
coda.sim.inm.long=read.coda("sim_inm.txt","sim_inm_Index.txt")

summary(coda.sim.inm.list)
summary(coda.sim.inm.long)

gelman.diag(coda.sim.inm.list)

plot(coda.sim.inm.list)
plot(coda.sim.inm.long)
cumuplot(coda.sim.inm.long)

# calculate maximum a posteriori estimates:
m1 <- as.matrix(sim.inm)
e <- calcmode(m1[,1][[1]])
x <- calcmode(m1[,1][[2]])
y <- calcmode(m1[,1][[3]])
b <- calcmode(m1[,1][[4]])
alpha <- calcmode(m1[,1][[5]])

}