mcmc_ds: Function for MCMC analysis

In hierarchicalDS: Functions to Perform Hierarchical Analysis of Distance Sampling Data

Description

Function for MCMC analysis

Usage

mcmc_ds(Par, Data, cur.iter, adapt, Control, DM.hab.pois,
  DM.hab.bern = NULL, DM.det, Q, Prior.pars, Meta)

Arguments

Par	A list comprised of the following parameters: "det": a vector giving the current iteration's linear model parameters for the detection model; "hab.pois": a vector giving the current iteration's linear model parameters for Poisson abundance intensity; each row gives parameters for a particular species "hab.bern": a vector giving the current iteration's linear model parameters for Bernoulli part of ZIP model for abundance (if Meta$ZIP=TRUE) "cor": a correlation parameter for detections that's an increasing function of distance (correlation at the maximum distance); "Nu": a vector giving the log of the abundance intensity for each strata; "Eta.pois": If Meta$spat.ind==FALSE, spatial random effects for Poisson abundance model; one for each cell and for each species "Eta.bern": If Meta$spat.ind==FALSE & Meta$ZIP=TRUE, spatial random effects for Bernoulli abundance model; one for each cell and for each species "tau.eta.pois": If Meta$spat.ind==FALSE, precision for spatial ICAR model(s) for the Poisson component "tau.eta.bern": If Meta$spat.ind==FALSE & Meta$ZIP=TRUE, precision for spatial ICAR model(s) for the Bernoulli component "tau.nu": Precision for Nu (overdispersion relative to the Poisson distribution) "G": a vector giving the number of groups of animals in each strata; "N": a vector giving the number of animals in each strata "MisID": a list, each entry i of which is a vector holding the parameters for the ith misID model "Cov.par": an (n.species X n X n.ind.cov) array holding parameters of individual covariate distributions.
Data	A four dimensional array; the first dimension gives species, the second gives the transect, the third indexes a (possible) observation, and the fourth dimension gives observations and covariates associated with a given animal. These final columns are: Observer ID,Y(observation=0/1),Observed species,Obs covariates,Distance,Ind covariates
cur.iter	Number of iterations to run
adapt	If adapt==TRUE, run MCMC in adapt mode, optimizing MCMC proposal distributions prior to primary MCMC
Control	A list object including the following objects: "iter": number of MCMC iterations; "burnin": number of MCMC burnin iterations; "thin": if specified, how many iterations to skip between recorded posterior samples; "adapt": if adapt==TRUE, this gives the number of additional MCMC iterations should be performed to adapt MCMC proposals to optimal ranges prior to final MCMC run; "MH.cor": Metropolis-hastings tuning parameter for updating the correlation parameter (if Meta$point.ind==TRUE); "MH.nu": MH tuning parameter for Nu parameters (Langevin-Hastings multivariate update); "RJ.N": A vector giving the maximum number of additions and deletions proposed in an iteration of the RJMCMC algorithm for each transect "iter.fix.N" Number of iterations to skip RJMCMC step
DM.hab.pois	A design matrix for the Poisson model for abundance intensity (log scale)
DM.hab.bern	If Meta$ZIP=TRUE, a design matrix for the Bernoulli zero model (probit scale)
DM.det	A design matrix for the probit of detection probability
Q	An inverse precision matrix for the spatial ICAR process
Prior.pars	A list object giving parameters of prior distribution. Includes the following objects "a.eta": alpha parameter for prior precision of spatial process (assumed Gamma(a.eta,b.eta)) "b.eta": beta parameter for prior precision of spatial process (assumed Gamma(a.eta,b.eta)) "a.nu": alpha parameter for prior precision of overdispersion process (assumed Gamma(a.nu,b.nu)) "b.nu": beta parameter for prior precision of overdispersion process (assumed Gamma(a.nu,b.nu)) "beta.tau": Prior precision for regression coefficients "misID.mu": a list vector, each entry gives normal prior means for misID regression coefficients for the corresponding model in Meta$misID.mat (can be set to null if no misID) "misID.sd": a list vector, each entry gives normal prior sd for misID regression coefficients for the corresponding model in Meta$misID.mat (can be set to null if no misID)
Meta	A list object giving a number of other features of the dataset, including: "n.transects" Number of transects "n.species" Number of species "S" Number of strata cells "spat.ind" Indicator for spatial dependence "Area.hab" Vector giving relative area covered by each strata "Area.trans" Vector giving fraction of area of relevant strata covered by each transect "Adj" Adjacency matrix giving connectivity of spatial grid cells "Mapping" Vector mapping each transect into a parent strata "Covered.area" Vector giving the fraction of each strata covered by transects "n.Observers" Vector giving the number of observers that operated on each transect "M" Matrix with species-specific rows giving maximum possible value for number of groups present in each transect (in practice just set high enough that values at M and above are never sampled during MCMC) and can be fine tuned as needed#' "stacked.names" Character vector giving column names for the dataset "factor.ind" Indicator vector specifying whether data columns are factors (1) or continuous (0) "detect" If TRUE, detection parameters are estimated; if FALSE assumes a census "Det.formula" a formula object specifying the model for the detection process "Levels" a list object, whose elements are comprised of detection model names; each element gives total # of levels in the combined dataset "i.binned" indicator for whether distances are recorded in bins (1) or are continuous (0) "dist.pl" gives the column in Data where distances are located "G.transect" vector holding current number of groups of animals present in area covered by each transect "N.transect" vector holding current number of animals present in covered area by each transect "grps" indicator for whether observations are for groups rather than individuals "n.bins" number of distance bins (provided i.binned=1) "Bin.length" vector giving relative size of distance bins "n.ind.cov" Number of individual covariates (distance is not included in this total, but group size is) "Cov.prior.pdf" character vector giving the probability density function associated with each individual covariate (type ? hierarchical_DS for more info) "Cov.prior.parms" An (n.species X n X n.ind.cov) array providing "pseudo-prior" parameters for individual covarate distributions (only the first row used if a signle parameter distribution) "Cov.prior.fixed" indicator vector for whether parameters of each covariate distribution should be fixed within estimation routine "Cov.prior.n" (#species X #covariates) Matrix giving number of parameters in each covariate pdf "ZIP" If TRUE, fit a ZIP model to abundance "point.ind" Indicator for whether point independence assumed (if no, then no correlation modeled b/w multiple observers as function of distance) "last.ind" If TRUE (and point.ind=TRUE), point independence operates by assuming 0 dependence at the farthest bin "cor.const" If TRUE, forces estimates of correlation associated with point independence to be positive if last.ind==FALSE or negative if last.ind==TRUE (default is FALSE) "fix.tau.nu" Indicator for whether tau.nu should be fixed (1) or estimated(0) "srr" Indicator for whether a spatially restricted regression model should be employed (1) or not (0) "srr.tol" Threshold eigenvalue level for SRR; only eigenvectors with higher eigenvalues than srr.tol are included in SRR formulation "misID" If TRUE, misidentification of species is modeled "misID.mat" With true state on rows and assigned state on column, each positive entry provides an index to misID.models (i.e. what model to assume on multinomial logit space); a 0 indicates an impossible assigment; a negative number designates which column is to be obtained via subtraction "misID.models" A formula vector providing linar model-type formulas for each positive value of misID.mat. "misID.symm" If TRUE, classification probabilities assumed to be symmetric (e.g. pi^2|1=pi^1|2) "N.par.misID" A vector specifying the number of parameters needed for each misID model "N.hab.pois.par" A vector specifying the number of parameters needed for each species' Poisson abundance model "N.hab.bern.par" If fitting a ZIP model, this vector specifying the number of parameters needed for each species' Bernoulli zero model "post.loss" If TRUE, observed and predicted detections are compiled for posterior predictive loss

Value

returns a list with the following objects: "MCMC": An 'mcmc' object (see 'coda' R package) containing posterior samples; "Accept": A list object indicating the number of proposals that were accepted for parameters updated via Metropolis- or Langevin-Hastings algorithms; "Control": A list object giving MCMC tuning parameters (which are updated if the 'adapt' alorithm is used) "Obs.N": Records latent abundance in each transect; dimension is (n.species X # samples X # transects) "Pred.N": Posterior predictive distribution for abundance in each transect; obtained by sampling a Poisson distribution given current parameter values (with possible zero inflation) "Post": Holds posterior samples for strata specific group sizes ("Post$G") and abundance ("Post$N") "Obs.det": if Meta$post.loss=TRUE, an array holding observed detection types for posterior predictive loss calculations dim = c(n.transects,n.obs.types,n.obs.types) "Pred.det": if Meta$post.loss=TRUE, an array holding predicted detection types for posterior predictive loss calculations dim = c(n.mcmc.iter,n.transects,n.obs.types,n.obs.types)

Author(s)

Paul B. Conn

hierarchicalDS documentation built on July 3, 2019, 1:07 a.m.