mcmc.conCatSMR.natural: Fit the categorical spatial mark resight model for natural...

In benaug/SPIM: This package contains MCMC algorithms in R and (some) Rcpp for various Spatial Partial Identity Models. Prospective users should email Ben before using.

Description

This function fits the conventional categorical spatial mark resight model when the number of marked individuals is unknown.The distribution of marked individuals across the landscape is assumed to be spatially uniform. This can be relaxed by modeling the marking process in the generalized spatial mark resight samplers. An extension of this sampler that allows detection function parameters to vary by the levels of one categorical covariate is located in mcmc.conCatSMR.df(). A version of this sampler for a known number of marked individuals is in mcmc.conCatSMR().

the data list should be formatted to match the list outputted by sim.conCatSMR(), but not all elements of that object are necessary. y.sight.marked, y.sight.unmarked, G.marked, and G.unmarked are necessary list elements. y.sight.x and G.x for x=unk and marke.noID are necessary if there are samples of unknown marked status or samples from marked samples without individual identities.

An element "X", a matrix of trap coordinates, an element "K", the integer number of occasions, and an element n.marked, the integer number of marked individuals are necessary.

IDlist is a list containing elements ncat and IDcovs. ncat is an integer for the number of categorical identity covariates and IDcovs is a list of length ncat with elements containing the values each categorical identity covariate may take.

An element "locs", an n.marked x nloc x 2 array of telemetry locations is optional. This array can have missing values if not all individuals have the same number of locations and the entry for individuals with no telemetry should all be missing values (coded NA).

I will write a function to build the data object with "secr-like" input in the near future.

If you need category level detection functions with an unknown number of marks, email Ben. He hasn't written this one, yet, but it will be easy to do.

Usage

mcmc.conCatSMR.natural(data, niter = 2400, nburn = 1200, nthin = 5,
  M1 = 30, M2 = 200, inits = NA, obstype = "poisson", nswap = NA,
  proppars = list(lam0 = 0.05, sigma = 0.1, sx = 0.2, sy = 0.2),
  storeLatent = TRUE, storeGamma = TRUE, IDup = "Gibbs", tf = NA,
  priors = NA)

Arguments

data	a data list as formatted by sim.conCatSMR(). See description for more details.
niter	the number of MCMC iterations to perform
nburn	the number of MCMC iterations to discard as burnin
nthin	the MCMC thinning interval. Keep every nthin iterations.
M1	the level of data augmentation for marked individuals
M2	the level of data augmentation for unmarked individuals
inits	a list of initial values for lam0, sigma, gamma, psi1, and psi2. The list element for gamma is itself a list with ncat elements. See the example below.
obstype	a character string indicating the observation model, "bernoulli" or "poisson".
nswap	an integer indicating how many samples for which the latent identities are updated on each iteration.
storeLatent	a logical indicator for whether or not the posteriors of the latent individual identities, z, and s are stored and returned
storeGamma	a logical indicator for whether or not the posteriors for gamma are stored and returned
IDup	a character string indicating whether the latent identity update is done by Gibbs or Metropolis- Hastings, "Gibbs", or "MH". For obstype="bernoulli", only "MH" is available because the full conditional is not known.
propars	a list of proposal distribution tuning parameters for lam0, sigma, s, and st, for the the activity centers of untelemetered and telemetered individuals, respectively. The tuning parameter should be smaller for individuals with telemetry and increasingly so as the number of locations per individual increases.

Author(s)

Ben Augustine

Examples

## Not run: library(coda)
N=50
n.marked=12
lam0=0.35
sigma=0.50
K=10 #number of occasions
buff=3 #state space buffer
X<- expand.grid(3:11,3:11) #make a trapping array
pMarkID=c(.8,.8)#probability of observing marked status of marked and unmarked individuals
pID=.8 #Probability marked individuals are identified
ncat=3  #number of ID categories
gamma=IDcovs=vector("list",ncat) #population frequencies of each category level. Assume equal here.
nlevels=rep(2,ncat) #number of levels per IDcat
for(i in 1:ncat){
  gamma[[i]]=rep(1/nlevels[i],nlevels[i])
  IDcovs[[i]]=1:nlevels[i]
}
pIDcat=rep(1,ncat)#category observation probabilities
tlocs=0 #telemetry locs/marked individual
obstype="poisson" #observation model, count or presence/absence?
marktype="natural" #premarked or natural ID (marked individuals must be captured)?
data=sim.conCatSMR(N=N,n.marked=n.marked,lam0=lam0,sigma=sigma,K=K,X=X,buff=buff,obstype=obstype,ncat=ncat,
                      pIDcat=pIDcat,gamma=gamma,IDcovs=IDcovs,pMarkID=pMarkID,tlocs=tlocs,pID=pID,marktype=marktype)
#MCMC
inits=list(lam0=lam0,sigma=sigma,gamma=gamma,psi1=0.5,psi2=0.5) #start at simulated values
proppars=list(lam0=0.1,sigma=0.08,s=0.5,st=0.08) #st only for telemetered inds. Should be smaller than s.
M1=50 #marked data augmentation
M2=100 #unmarked data augmentation
storeLatent=TRUE
storeGamma=FALSE
niter=1000
nburn=0
nthin=1
IDup="Gibbs"
out=mcmc.conCatSMR.natural(data,niter=niter,nburn=nburn, nthin=nthin, M1 = M1,M2=M2, inits=inits,obstype=obstype,
                              proppars=proppars,storeLatent=TRUE,storeGamma=TRUE,IDup=IDup)


plot(mcmc(out$out))

1-rejectionRate(mcmc(out$out)) #shoot for 0.2 - 0.4 for lam0 and sigma. If too low, raise proppar. If too high, lower proppar.
1-rejectionRate(mcmc(out$s1xout)) #marked activity center acceptance in x dimension. Shoot for min of 0.2
1-rejectionRate(mcmc(out$s2xout)) #unmarked activity center acceptance in x dimension. Shoot for min of 0.2

#Example for regular conventional SMR (no identity covariates)
N=50
n.marked=12
lam0=0.35
sigma=0.50
K=10 #number of occasions
buff=3 #state space buffer
X<- expand.grid(3:11,3:11) #make a trapping array
pMarkID=c(.8,.8)#probability of observing marked status of marked and unmarked individuals
pID=.8 #Probability marked individuals are identified
ncat=1  #number of ID categories
gamma=IDcovs=vector("list",ncat) #population frequencies of each category level. Assume equal here.
nlevels=rep(1,ncat) #number of levels per IDcat
for(i in 1:ncat){
  gamma[[i]]=rep(1/nlevels[i],nlevels[i])
  IDcovs[[i]]=1:nlevels[i]
}
pIDcat=rep(1,ncat)#category observation probabilities
tlocs=0 #telemetry locs/marked individual
obstype="poisson" #observation model, count or presence/absence?
marktype="natural" #premarked or natural ID (marked individuals must be captured)?
data=sim.conCatSMR(N=N,n.marked=n.marked,lam0=lam0,sigma=sigma,K=K,X=X,buff=buff,obstype=obstype,ncat=ncat,
                      pIDcat=pIDcat,gamma=gamma,IDcovs=IDcovs,pMarkID=pMarkID,tlocs=tlocs,pID=pID,marktype=marktype)
#MCMC
inits=list(lam0=lam0,sigma=sigma,gamma=gamma,psi1=0.5,psi2=0.5) #start at simulated values
proppars=list(lam0=0.1,sigma=0.08,s=0.5,st=0.08) #st only for telemetered inds. Should be smaller than s.
M1=50 #marked data augmentation
M2=100 #unmarked data augmentation
storeLatent=TRUE
storeGamma=FALSE
niter=1000
nburn=0
nthin=1
IDup="Gibbs"
out=mcmc.conCatSMR.natural(data,niter=niter,nburn=nburn, nthin=nthin, M1 = M1,M2=M2, inits=inits,obstype=obstype,
                              proppars=proppars,storeLatent=TRUE,storeGamma=TRUE,IDup=IDup)


plot(mcmc(out$out))

## End(Not run)

benaug/SPIM documentation built on Jan. 23, 2022, 4:29 a.m.